See Wikipedia on the RSA problem and in particular Breaking RSA may not be equivalent to factoring - which actually shows it's a lot less likely than you might think that anyone is going to prove breaking RSA equivalent to integer factorization.

No cryptosystem that can be cracked given unbounded computing power can currently be "proven secure" since we're a long way from showing that any useful problem is computationally hard. The best you can do is show that it's hard given some assumption.

Not wishing to be rude, but what caused such incredible overconfidence that you would say

I believe RSA can only be cracked by prime factorisation with the same certainty that I believe the primes are infinite. The only scenario in which they are false is one in which I am insane.

without personally understanding a proof to that effect? I do personally understand a proof that certain Rabin-based cryptosystems are as hard as integer factorization to break, and I'm still less confident of their theoretical security than I am of the infinitude of primes.

EDITED TO ADD: I should put a massive caveat on my assertions about Rabin before anyone gets the wrong impression: the proof that the cryptosystem is as hard as factoring depend on what is known as the "random oracle model", which is a very useful but unrealistically strong assumption about our hash functions.

just edit it.