I know how it's called and I know what a Greek phoenix is. But Marco's fruit has properties that can't be attributed to the Greek phoenix. And, as I said, the phoenix is probably the most globalized creature and therefore the fenghuang/hou-ou has lost many of its uniqueness by adopting certain traits of the Greek version. This is why Marco's fruit is actually the worst counter-example possible to the argument of mythical zoans being Eastern creatures, because the Eastern phoenix has been changed in order to "please" modern audiences to the point of assimilating some characteristics of its Western "counterpart". The best known example of this may be the pokémon Ho-oh, who albeit keeping traits of its namesake from real world mythology has adopted properties of the Greek phoenix such as the solid igneous nature (Fire type) and the power of being reborn from its own ash (ability Regenerator).
At this point, the fenghuang is basically treated by the world as "the Chinese phoenix", same for the hou-ou in Japan, therefore making sense for Oda to call Marco's fruit like that. Modern world has phagocytized the differences between them and has made them comparable, maybe because, although not so directly, the Eastern animal contains certain attributes of fire and immortality too. This has also happened to the dragon, albeit in a lesser degree, hence why some people confuse the Eastern and Western dragons in threads about Kaido's fruit (even though Kaido is full of the symbolic traits of the Eastern one and virtually none of the Western).
Again, as I said, Marco can't be used as a case for non-Eastern mythical zoan. Not only for what I just explained, but also because he actually has obvious traits from the Eastern phoenix. His tail, his comparison to a rooster/pheasant, his colors ("phoenix" etymology contains the word "red" because it is a vermilion bird while Marco's combination of blue, yellow, violet... fit a fenghuang more), his personality, even the fire and immortality properties. Basically it could be argued that Marco is more of a fenghuang than a Greek phoenix. So it makes no sense to use him to support hypothetical fruits such as the manticore, the chimera, Cerberus, an angel and so on, which have zero relation with Japan (and around) and haven't been assimilated by Eastern counterparts.