Couple of things come... we can define, and re-define, the term 'center' based on many postulates, but that doesn't change what I theorized. I used the word 'relatively', and relatively it's mathematically sound for any point to claim 'center' status... the laws of physics are still in place for each 'relative' point.
You say:
"You can say, but it seems that way in terms of my perspective, but that's just as true of everyone else. That's the same as saying the earth looks flat when you look at it from your own vantage point. Okay, but...it isn't."..
that's true and false. The first and second sentence are almost exactly what I said... but it's nothing like saying "the earth is flat" because that defies physics. I'm not defying physics from my office chair... if I say my chair is hotter than the sun I am.
Most, (not all), of what I read uses "Mass" of the known universe as way to speculate about the "center". But, and as you point out, in a way, that's an unknown. It simply helps us to understand structure better by setting a base point, but doesn't have to be "Mass"... it could be spatial distance which may or may not coinincide with mass.
I understand why physicists love the phrase.. it helps in portraying the real grandeur that is the Universe - that there is so much beyond us.... but I don't think it's a 'mathematical' claim. - JamesJM