What exactly were we fabricating? I think it's accurate to say that Macedon was a Hellenized nation not part of Greece proper. They've been considered separate entities for most of their existence, while Philip and Alexander were considered foreigners by the Greeks themselves.
Thing 1: There was basically no solid definition of "Greek" except for "dudes who speak Greek" in the exact meaning of the word barbaroi. Alex and Phil spoke Greek. You'd think that that'd involve a "Q.E.D." or something. It's not like they had to pick up a passport from the post office or something. But they had the next closest thing:
Thing 2: The Argeades' founding identity centered around the presumption of direct descent from people who spoke Greek. This does not typically define ethnicity in the strictest sense, but it was enough of an argument to get the only thing close to a panhellenic institution, the Olympian games, to admit Alex and Phil:
regardless of differences between the supposed "original" Makedonians and Greeks, the royal family was basically as Greek as it gets. This seems relevant. Both of these Things, incidentally, are widely known and should have stopped pretty much any argument. There wasn't a very firm "Greek" identity, but insofar as there was, it had two meaningful criteria and both Alex and Phil fit both of them. Moving on.
Thing 3: Typically, grousing about Greek-Mak differences is overblown. Maybe 75% of that comes from the accounts of the life of Eumenes of Kardia, noted Thracian Greek notable, member of the Makedonian aristocracy, and Alex's secretary. Eumenes' favorite card to play in his speeches, per Hieronymos (also an inhabitant of Kardia), was how he was a Greek, not like the soldiers he led or the generals he fought or the king he had served before his "untimely" death. Surprisingly (hur dur) this did not impact his ability to actually motivate these men and retain their loyalty - arguably, his urMesogaian Mak opponents had
more such issues (e.g. Antigonos). The conclusion of most of the modern accounts of Eumenes' career is that he played it up for rhetorical effect, not because it was actually indicative of meaningful ethnic differences.
Thing 4: Furthermore, the accounts of Eumenes' speeches themselves blow most claims of a separate Makedonian language unrelated to (and unintelligible with) Greek out of the water - the remaining 25% comes out of a famous scene during the conquest of Iran, when Alexander convenes a trial which is supposed to be conducted wholly in the "Makedonian language" but in which only Greek words are actually mentioned. Not exactly good ammunition, there. Was there an ancient Makedonian language that was unrelated to Greek? Maybe, but if it existed there's basically no trace of it by the fourth century BC, and even if it did it certainly doesn't impact the supposed Greekness of Alex or Phil. Even if we go with the most extreme potential reading, that the Maks were basically a completely foreign people who wandered in around 900 BC or so (hell, let's make them Slavs for kicks and giggles) and who ended up speaking Greek by the fourth century, how does that make them any different from supposed Greeks like
every Dorian ever? Are we going to decide that the Spartans weren't Greek either?