Not to criticize your question--which I will answer--but right off the bat, you might want to tone down your assumptions. I know it's fashionable to bash school curricula, but in this case, it's possibly unwise. I can't speak for every elementary system, but I can speak for California's state curriculum as it relates to the subject, and California is one of the larger school systems in the world, so:

Ahem. The ancient world is first broached in 7th grade, and at present, while narratives like Thermoplyae may be shared by individual (uninspired) teachers, the state has this to say of Persia: ": Over the centuries, the cities of Mesopotamia were divided into multiple states, conquered by invaders, and combined into new states. While it is not possible to teach all the states and groups that ruled over Mesopotamia, it is critical that students understand the importance of the Persian Empire. The names of the empire changed often with changes in the ruling groups (Achaemenids, Seleucids, Parthians, Sasanians), but the Persian Empire maintained its continuity and its domination over Mesopotamia, Persia, and often wide areas of southwestern Asia and Egypt, from c. 500 BCE to c. 630 CE. It was the primary political and cultural presence in western Asia during that period. Because the Persians fought wars with the ancient Greeks, Greek writers often criticized the Persians. However, the Persian ruled over a very large empire, from the Aegean Sea to the Indus River, with policies of multicultural tolerance."

Which is hardly characterizing them as tyrannical, and in fact stresses that Persia's was the much more influential region. It later goes on to stress, possibly to correct teachers not well-versed in the era, that "As the main heir of Mesopotamian civilization, the Persian Empire played as large a role in world history as the Greeks or Romans."

So assuming your teacher is reasonably well-trained (which I admit is not always a safe assumption) your children really shouldn't be seeing 300 as anything other than a mindless action flick.

As to your question: Your assumption is mooostly correct. Greece as a region was not crucial to the Persian empire; it was more than wealthy and populous enough without the Greek colonies. However, during the Greco-Persian wars, they were certainly at the fore of Persian attention, and rightfully so. Persia was vast and in many ways advanced, but recall that it would be invaded successfully by a largely-Greek army less than a century after the Greco-Persians wars! Now, there's a lot to say about this period--most notably, that it really wasn't always a team of Greeks fighting a team of Persians. The politics were often individual, and many Greeks fought for the Persians at various times. One of the more popular 'ends' of the period was when the Spartan-led coalition accepted peace with Persia by more or less ceding the Ionian greek colonies--Sparta having decided hegemony was worth giving up what was the essentially the point of the wars. '

This being one of the most-studied periods in western history, period, there's a staggering amount to say about it, so let me recommend almost any of the works of Peter Green--they're easily accessible and solid overviews of the period. Of course, they're also more Greek than Persian in sourcing. For that, I'd recommend Tom Holland's Persian Fire. Holland himself isn't without controversy, but the book was excellent, and gives a more engaging answer to your question than I can! (And he's surely more succinct.)