So, I base the question on this passage from the Dirgha Nikaya (that's Digha for you Theravadis! )
There are various kinds of assemblies, O Ananda; assemblies of nobles, of Brahmans, of householders, of bhikkhus and of other beings.
When I used to enter an assembly, I always became, before I seated myself, in color like unto the color of my audience and in voice like unto their voice. I spoke unto them in their language and then with religious discourse, I instructed, quickened, and gladdened them.
But when I spoke, they knew me not and would say, Who may this be who thus speaks, a man or a god?
Then having instructed, quickened, and gladdened them with religious discourse, I would vanish away. But they knew me not, even when I vanished away
Buddha also said in the Sundarika Bharadavaja sutta (SN 3.4), that he was a counsellor and went around the world!
So which teachings do you think are Buddha's???