Here's how we can tell:
It arrived from Hoenn. This means that it had to be legally obtained through a Generation III distribution. Here are the ID/ID numbers the event Mew had:
ハドウ - 50716
ポケパーク - 60510
MYSTRY - 06930
Aura - 20078
None of them are "TATA" or 16199.
You got it from the GTS. Mystical Pokemon (Mew, Celebi, Jirachi, Deoxys, Manaphy, Darkrai, Shaymin, Arceus, Victini, Keldeo, Meloetta, Genesect, Diancie) cannot be traded across the GTS.
These two things guarantee your Mew is unauthentic.
Source: Above Link, and cross-referencing! o3o