I think it's a bit more than maybe. He says he's at Babylon, and Rev 17 shows that Babylon was identified by John as Rome. I think the best way to approach this Scripturally is to assume Peter means Rome unless and until contrary evidence is found.
And you're right, he doesn't say anything about primacy in his epistle. We get that from other texts.
Is it meaningless to you that I never claimed "it ain't in Scripture so it can't be true"? Please make a good faith effort to stick to the facts.
It is not meaningless at all...I thought you were implying that if Peter in Rome was not Scriptural, then I had no basis for saying it. My apologies that I misrepresented your position.