You are tacitly assuming that Platonists have to hold that what is formally true (proveable, derivable from axioms) is actuallty true. But a significant part of the content of Platonism is that mathematical statements are only really true if they correspond to the organisation of Plato's heaven. Platonists can say, "I know you proved that, but it isn't actually true". So there are indeed different notions of truth at play here.

Which is not to defend Platonism. The notion of a "real truth" which can't be publically assessed or agreed upon in the way that formal proof can be is quite problematical.