I'd like to clarify this terminology a bit. 

When I think of your three examples, yes the word irrelevant comes to mind.  The issuer of the paper, the spell checker, and the short name of the curve, are all things which I don't even need to know to use bitcoin or to write my own client.  One might even say "provably" irrelevant for that reason, in that the relevance in question here implied by the forum in which we are using.  However I personally would avoid using that terminology, perhaps because of my mathematics background.   

However the G points are hardly irrelevant in this context, please correct me if I am wrong.  If I don't know them I can't validate TXs, can't sign TXs, and so I can't use bitcoin at all.  Every ECC operation in bitcoin requires every bit of G to be exactly right.  When you say G is provably irrelevant, I can only assume (and I'd rather not hence this reply) that you mean a choice of G cannot effect the ability of an attacker to brute force a private key.  While there are convincing arguments of that in this thread, I wouldn't call any of them a proof.  AFAIK the difficulty of discrete logs, on elliptic curves, or even the difficulty in factoring large numbers, has not been proven and probably a proof that these things cannot be done in polynomial time would be equivalent to a proof that P!=NP.