https://en.wikipedia.org/wiki/Social_War_(91%E2%80%9388_BC)
It wasn't until the early 1800s that a group of nationalists and aristocrats started a nationalist movement.
https://en.wikipedia.org/wiki/Italy#Italian_unification
Greek nationalism developed around the same time. Before that, the territory that is modern Greece passed in large pieces between different empires and the Catholic church. Previous to that the Polis or city state was the highest political authority and the unit of place identity. There was some flirtation with larger alliances like those that fought the Peloponnesian War but they were loose and did not last after outside conquest.
"Greek nationalism developed around the same time."
This not true.
While the 'nation state' as a legal formalism didn't arrive until recently - the 'Greek identity' existed in antiquity.
Not only that - Greek identity was maintained throughout 2000 years of occupation!
That's how strong and 'not arbitrary' their cultural foundation is.
If smaller Greek states were 'arbitrary' - they would have evaporated during Roman occupation. But an entity the Romans called 'Graecia' (sound familiar?) changed hands several times throughout history - more or less intact as a people and culture.
Though Greece was a collection of smaller states, and never a unified entity - they shared very similar cultural foundations, which were distinct from those around them (most of which changed and/or evaporated).
When the Persians invaded 'Greece' - the infighting Greek states bound together and acted more or less as an entity to push out the invaders.
Point being: 'Invading Persians' was not the same thing as 'Spartans invading Athens'.
Nation states were not arbitrarily formed, they are mostly ethnically oriented, and some of the boundaries have not changed in eons.
The thesis that 'nation states are arbitrary' is easily dismissed by having a look at maps of Europe throughout time. The state of Sweden is not some random thing, it's where 'the Swedes' live - roughly.
If the lines were 'arbitrary' - we'd see a mishmash of weird lines, crossing ethnicities - much like the somewhat arbitrary divisions between Syria, Iraq, Kuwait etc..
But they are not.
Funny enough, I think the legal IP questions of this article have nothing to do with this issue! For once, we're dealing with a more secular, legal thing, I think.
Summary: 'Graecia' was Greece literally more than 2000 years ago, the formation of a 'Greek state' is not arbitrary.
You're reading an awful lot into a single anecdote. There were other occasions where some Greek polities allied with Persians against others.
I can't speak for Greece, but Italy is a really BAD example of a "naturally arisen" national identity. In fact the (now second party) Northern League's sole purpose until Matteo Salvini was to split Northen Italy from the south.
Source: British person living in Northern Italy with many friends from the South.
That was the agenda, then of course there are a lot of declinations the whole thing took. Like, as an example, members and sustainer of the Northern League considering the people from the south as "not Italians", derogatorily addressing them as "terroni" and so forth.
Then along came Salvini, who switched the focus from the south of Italy to the refugees, making them the enemy now. And the rest is pretty much in the daily news.
So no, sir, you did not overstate it.