I have answered similar questions in this sub before here and here.

Middlekauff's book itself discusses the reasoning a little bit before the passage you quoted:

This “unofficial” colonial position was a good deal clearer when it dealt with the internal sphere than the external. It held that since the colonials as Englishmen were born free, a contention with Lockeian overtones, they were subject only to laws made with their own consent. Moreover, their rights had received royal approval through the various charters issued to the colonies. Although these charters amplified and extended these rights, they did not provide an absolute basis for them. The colonists were English, and Englishmen could be governed only by their own consent given through their own representatives.

The question of why the colonists were subject to any regulation by Parliament, or just what constituted the external sphere, interested these colonial writers much less.

And:

The charters issued to the colonies by the Crown appeared to be made of more solid stuff, but despite a number of flat statements that they incorporated fundamental rights, including the right to be taxed only by one’s representatives, there was an uneasy recognition in these assertions that the Crown had vacated them in the past and might do so again/

Yet even with all these uncertainties about the nature of the constitution, a half-articulated constitutionalism made its appearance by 1766. It held that there were limits, outside of and independent of Parliament. Their essence might not be altogether clear and their sources might be a matter of dispute, but they existed nonetheless.

The fact remained, however, that the American colonies were a part of the empire, and an argument that Parliament, like all political bodies, was limited did not establish where its legal lines of jurisdiction began and ended.

The Massachusetts Circular he is referring to in the passage you quoted also discusses it; you can read the text of it here.

In short, Massachusetts, and, later, the other colonies, argued that they already had the unilateral right to tax their citizens, solely through their local colonial legislature. In Massachusetts, this legislature was known as the "Massachusetts General Court". This had been granted to them in their 1691 charter, still in effect in the 1760s and 70s (spelling and punctuation updates mine):

"...And we do for us, our Heirs, and Successors, Give and grant that the said General Court or Assembly shall have full power and Authority to...impose and levy proportionable and reasonable Assessments, Rates, and Taxes upon the Estates and Persons of all and every the Proprietors and Inhabitants of our said Province or Territory to be Issued and disposed of by Warrant under the hand of the Governor..."

The Massachusetts Circular makes it a point that giving Massahcusetts seats in Parliament was impractical because of the distance involved, but further, it talks about the "equity" of doing it.

And that's the important point. It was Massachusetts' position, and later the position of the other colonies, that their legislatures were co-equal with Parliament already under the terms of the colonial charters. But they also argued that this did not rely on the language in the charter alone, but that the rights of Englishmen (per their reading of the English Bill of Rights of 1689, among other documents) entitled them to these rights regardless. That is, the only way Parliament could tax a colony is through the consent of the governed, and the only legal way for the colonists to give that consent at that time was through their local colonial legislature, when the legislature voted in favor. Otherwise, Parliament had no unilateral right to tax them; the colonial legislatures had the right to veto it.

This whole idea, of "popular sovereignty", that these rights derive from the consent of the people, is the fundamental principle that the Declaration of Independence and U.S. Constitution are based upon. English law, on the other hand, is based on the principle of "Parliamentary supremacy", that Parliament is the law, and what they say goes. Parliament could argue that the colonial charters were only in effect as long as Parliament said they were, because they'd revoked them before--and they'd revoke them again. The Massachusetts Government Act was passed in 1774, was one of the "Intolerable Acts", and revoked Massachusetts' charter and put the colony under martial law. The Intolerable Acts were essentially what led directly to the Revolutionary War, and the act is cited as one of the grievances in the Declaration of Independence.

Massachusetts understood that Parliament had revoked the charter before, hence their reliance on "the rights of Englishmen" that derived more constitutionally than from the charter alone. This argument is made in the Massachusetts Circular. Benjamin Franklin also made the argument in testimony before the House of Commons in relation to the Stamp Act:

Q. Don’t you know that there is, in the Pennsylvania charter, an express reservation of the right of parliament to lay taxes there?

A. I know there is a clause in the charter, by which the King grants that he will levy no taxes on the inhabitants, unless it be with the consent of the assembly, or by act of parliament.

Q. How then could the assembly of Pennsylvania assert, that laying a tax on them by the stamp-act was an infringement of their rights?

A. They understand it thus; by the same charter, and otherwise, they are intitled to all the privileges and liberties of Englishmen; they find in the great charters, and the petition and declaration of rights, that one of the privileges of English subjects is, that they are not to be taxed but by their common consent; they have therefore relied upon it, from the first settlement of the province, that the parliament never would, nor could, by colour of that clause in the charter, assume a right of taxing them, till it had qualified itself to exercise such right, by admitting representatives from the people to be taxed, who ought to make a part of that common consent.

Q. Are there any words in the charter that justify that construction?

A. The common rights of Englishmen, as declared by Magna Charta, and the petition of right, all justify it.

When it came to the "Parliamentary supremacy" vs. "Popular soveriegnty" question, Massachusetts actually did have an argument to make. The original colony of Plymouth had operated under the Mayflower Compact, which was written en route to America, and signed only by the passengers on board. Neither the King nor Parliament were party to this original charter. The crown did send over an after-the-fact charter once the colony was successfully established, but the colony ignored it and continued to operate under the Mayflower Compact. That is, until the Glorious Revolution, when James II revoked all the charters in New England, New York, and New Jersey, and tried to form them into the "Dominion of New England" with the purpose of putting them under Catholic rule. The people in Boston revolted, and took the governor hostage. A new charter was then issued once James II had been overthrown back in England, which was the 1691 charter. It combined Massachusetts and Plymouth into a single colony, and while the crown was party to that charter, Massachusetts could argue it only came about because "we, the people" agreed to it. Immediately before, when revoking their charter which they had not agreed to, it had resulted in a justifiable overthrow of the government.

In 1754, there had actually been a deliberate and explicit effort by come colonists at the Albany Congress to get the colonies representation in Parliament, in exchange for giving up some of these chartered rights, like the right of taxation. But this effort didn't get much support. As far as the majority were concerned, they already had these rights. Getting a few token seats in Parliament wouldn't help protect their rights. It was sure to see them taken away. There was some talk about giving the colonies a sort of single presiding officer as their representative in Parliament, who then would have a veto power over taxation and other legislation in Parliament insofar as it affected the colonies. But this didn't go anywhere, either, because it was a plan that Parliament was sure to reject.

cont'd...