This was part of it, but it would be wrong to say that it was the "biggest reason" that Americans supported revolution. I don't think you can point to any single reason as the "biggest reason" for the Revolution. Rather, the most direct reason is a series of laws passed by British Parliament known as the "Coercive Acts" or "Intolerable Acts". The comment you are quoting (whether they know it or not) are referencing one of the acts often lumped in with the Intolerable Acts—the Quebec Act. But that comment gives a rather selective interpretation of why this particular Intolerable Act was, er, intolerable.

Going back a bit, after the French agreed to a treaty at the end of the French and Indian War, there continued to be warfare between British Americans and the Native American nations that had allied with the French. This was known as Pontiac's War. The British attempted to enforce a ceasefire through an act of the King, known as the Royal Proclamation of 1763. The British Americans largely ignored it at first, Pontiac's Confederacy responded in kind, and it wasn't until the 1766 Treaty of Fort Ontario that a ceasefire was actually accomplished.

Nevertheless, this 1763 Royal Proclamation created what is known as the "Proclamation Line". For the time being, the British promised not to settle west of a line that essentially ran along the line of the Appalachian Mountains. Now, this did cause some animosity between some Americans (particularly among the Virginia aristocracy) and the British government. One of the central goals of the French and Indian War had been to gain an undisputed land claim of those Western lands, and force the French to give up their competing land claims. A group of Virginia aristocrats had been granted a real estate monopoly by the British government over that land, via their chartered rights (bought and paid for) of the Ohio Company of Virginia. The company was given exclusive authority to negotiate with Native American nations to purchase land out west, and once accomplished, they, in turn, could sell the land to interested buyers (farmers looking for cheap, good farmland). The Royal Proclamation prevented the investors in the Virginia Company from cashing in on their investment. The win against the French in the French and Indian War had not got them what they'd fought the war for.

However, this Proclamation Line was never meant to be permanent—at least, not from the British government's perspective. The British had no intention of permanently halting expansion. The intention of the British government was to prevent American colonists from squatting on land that hadn't yet been purchased (which the Royal Proclamation didn't entirely prevent). This way, they wouldn't have to fight further wars with Native Americans to get control of the land, but could instead gain possession through peaceful negotiation and purchase (the coercive nature of any such "purchase" is another matter for another post). So, the immediate outcome, in fact, was to begin purchasing land still in dispute east of the Proclamation Line, and "remove" the remaining Native American nations in the east to lands west of the line. Expansion westward would then come later, but the halt on expansion was only ever meant to be temporary.

The beginning of this path forward began well before the Revolution, with the negotiation of various treaties, the most important of which was the Treaty of Fort Stanwix in 1768. The Iroquois Confederacy ceded all their land claims in eastern New York and Pennsylvania as well as what is now West Virginia and Kentucky (a controversial point, since the Iroquois Confederacy didn't actually control much land in that area). Land north and west of the Ohio River would remain under Native American control—though the treaty didn't prevent the future purchase of such lands by British Americans. So, while it's debated among academics just how much influence the Royal Proclamation of 1763 contributed to the cause of the Revolutionary War, what isn't in dispute was that there was already quite a lot of new land that the American colonies gained control of in the 1760s and early 1770s that they could start selling to willing American settlers. The British government may not have yet gained, nor allowed, access to all the land promised to the Ohio Company, but the Ohio Company's investors had already got some of what they wanted, even if to gain control they had to cross other Native American nations that had not been signatories of the Treaty of Fort Stanwix.

And cross them they did. With the Treaty of Fort Stanwix and some subsequent treaties, squatters began moving onto Virginia's land claims in West Virginia and Kentucky—and even into modern day Ohio, which was not part of the treaty. The Shawnee and Mingo nations who claimed that land, and who hadn't been signatories to any of the treaties of the 1760s, attempted to stop this. Virginia then called out the militia, leading to Lord Dunmore's War, under which Virginia attempted to enforce their land claims in this area against any Native American nation who tried to claim otherwise.

In summary so far: after the French and Indian War, there was conflict over the colonization by British Americans of land west of the Appalachian Mountains. There were efforts by the British government and British/British American negotiators to gain control of this land peacefully. Some of these efforts had been successful, but some Americans, particularly in Virginia, were aggressively trying to take possession of land that had not yet been acquired by the British. That's what the British government was upset about. They weren't upset about expansion happening; they were upset that it was happening illegally and too soon.

This leads to that Intolerable Act mentioned at the top of this post—the Quebec Act. The cynics usually characterize the American reaction to this act as one being primarily motivated by greed over trying to take possession of Native American land. Most academic analysis, however, will tell you there were multiple purposes to this act. In part, there is a valid case to be made that British Parliament passed the act in order to stop Virginia squatters from crossing the Ohio River to illegally try to take possession of land the British did not own, in order to prevent yet another war with Native Americans. But the primary purpose of the Act had more to do with discontent among the French Canadiens of Quebec.

After gaining possession of Quebec at the end of the French and Indian War, the British government had tried to abolish French civil law and replace it with British law, which, among other things, included the requirement of a loyalty oath to the King of England. At that time, it meant recognizing the King as the head of the church, and renouncing the Catholic church and the Pope. This, effectively, disenfranchised most French Canadiens from either voting or holding public office. With major conflict with Massachusetts already underway threatening revolution, British Parliament feared that this movement would spread to the French Canadiens as well. So the Quebec Act's primary purpose was to stave off the discontent among the French Canadiens: it modified the loyalty oath to better enfranchise Catholics, it allowed for French-style civil law to be used in the province, and generally, it softened the hard line the British government had taken in the aftermath of the French and Indian War. But not only that, it granted to Quebec a bunch of land claimed by Virginia, i.e., all the land north of the Ohio River (still in possession of Native Americans by treaty, but now it would be Quebec who could negotiate to purchase that land, not Virginia).

Some scholars point out that the Treaty of Fort Stanwix and Royal Proclamation had effectively already taken away any claim of land north of the Ohio River that Virginia had. Pennsylvania and Quebec both claimed parts of this land, too, but the British government was content to resolve it another day—that day being the day Parliament passed the Quebec Act. Thus, the Quebec Act certainly made it clear that Virginia's claim was not going to be honored, if it hadn't been made clear before.

As far as British law went, Virginia had a convincing case to be made that this was illegal. Their colonial charter had granted them the land. Never mind that the charter of Pennsylvania somewhat overlapped on the western boundaries, but Quebec was only recently a British possession, so Virginian investors in the Ohio Company believed they were illegally being cheated out of land that the British crown had no legal authority to unilaterally hand over to the French Canadiens.

Thus, the Quebec Act, as one of these "Intolerable Acts", was cited as one of the grievances against the King in the Declaration of Independence:

For abolishing the free System of English Laws in a neighbouring Province, establishing therein an Arbitrary government, and enlarging its Boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule into these Colonies

cont'd...