This video is clearly trying to make a provocative point, and this determines its choice of what to talk about and how to present it. That said, I would say the video is broadly accurate. It contains numerous errors (there was no "farmer" class in Sparta; there was no property requirement for voting rights at Athens; the Dekeleian War is confused with the Corinthian War; the battle of Issos is confused with the battle of Ipsos; etc.) but these errors don't really affect the main argument.

While I wouldn't want to claim (as the video does) that Persia was a champion of freedom battling the tyrannical Greeks, I have argued previously that the Persian Empire tended to permit local autonomy to its subjects while allowing access to a vast network of trade and knowledge, offering advantages to those living under its sway. As such, the Persians have some claim to being a force of peace, prosperity and civilization in the Ancient World, like the Roman Empire is often thought to be in Western tradition. The tribute they levied in return was not considered unreasonable even by the Greeks; when the Athenians "liberated" Ionia, they set the tribute for this new part of their empire at the same level it had been under the Persians. It is certainly wrong to portray the Persians as a dark force of evil seeking to subject the world to slavery and destitution.

Meanwhile there are good reasons to question whether the cities of Greece were really the light of the free world. Sparta was indeed built on the exploitation of a vast slave class, who had no rights and were surpressed ruthlessly. Other cities and regions, too, had known such dependent populations, and all relied on considerable numbers of slaves to provide labour throughout Antiquity. While Athens gave voting rights to all adult male citizens (and actively denied those rights to the remaining 80-90% of the population), many other cities were ruled by oligarchies, in which the rich had all the power. Many others (especially in Sicily) were ruled by actual tyrants. The actual form of government of each state had more to do with political expedience and the balance of power between rich and poor than with any ideals about what a political system should be like. In practice, even in the most democratic Greek states, power remained largely in the hands of a few influential leisure-class clans, like the Alkmaionids at Athens. Of course, the Greeks seem to have been the first to enact legislation to involve common people in politics and to formulate concepts like isonomia (equality) and parrhesia (freedom of speech). Yet their world was defined by inequality and unfreedom. The only reason we think of them as free and enlightened is because our sources tend to focus on the lucky few, the wealthy adult male citizens, who were indeed free and sometimes enlightened.

As for relations between Greeks and Persians, it's important to stress that the alliance of 32 city-states against Persia was the first and only coalition of such size that the Greeks ever mustered, unless we count the mythical army of Agamemnon. Ancient Greece was not united. It was not a nation, let alone a nation-state. It consisted of hundreds of little states in which people spoke different dialects, had different cults and customs, and constantly fought each other. The brief alliance of some of them against Persia was rightly regarded even by the Greeks themselves as an anomaly; Herodotos stresses constantly how many of the Greeks actually chose the Persian side or simply refused to cooperate with the defenders of Greece.

Athens and Sparta were no exception. Shortly before the Persians invaded Greece, Sparta invaded Athens four times in an attempt to set up a pro-Spartan government; in the last few of these invasions, their explicit goal was to overthrow the democracy. Sparta and Athens were allies against Persia, but after the victory, relations soon turned sour; by 465 BC the alliance was broken, and Sparta and Athens were enemies during the First Peloponnesian War (461-446 BC), the Archidamian War (431-421 BC), the Dekeleian War (414-404 BC), the Corinthian War (395-386 BC) and the Boiotian War (378-371 BC). After that, they became allies against Thebes.

These constant wars for hegemony in Greece were gleefully exploited by the Persians, who were perfectly happy to support one side against the other if it meant that the Greeks would keep fighting each other rather than being a nuisance to Persia. Their policy was 'divide and rule' at its finest. To fight their long and bitter wars, the Greeks needed money; the Persians had plenty of it, and offered it freely to whoever could make sure that Greece would remain divided and weak. In the Dekeleian War, they funded the Spartan fleet, so that it could finally destroy the naval supremacy of Athens; in the process, the Persians recovered the Greek city-states of Asia Minor and reincorprated them into their empire. When Sparta turned against them, however, they funded the Athenian resurgence during the Corinthian War, which led to the dismantling of the Spartan empire. From this time onward, the Greeks regularly sent envoys to the Persian court to request Persian interference in their wars. Most Greek wars of the early 4th century BC ended with a "King's Peace", which was effectively an ultimatum sent by the Persians, that the Greeks were to cease fighting or else the Persians would take sides. It is entirely possible to argue that the Persians, after their failure to conquer Greece by military means, used money and diplomacy to turn it into a dependent region at the fringe of their empire.