It's definitely not proven to be correct; we definitely don't know for sure that integer factorization is in NP-hard. If I remember correctly, it's generally suspected that factorization is not NP-complete (and thus outside of NP-hard).

Wikipedia has it first on their "list of problems that might be NP-intermediate", i.e. problems that are in NP but not in P or NP-hard. [0]

[0] https://en.wikipedia.org/wiki/NP-intermediate