"You are correct with the consequences of my logic."
Well, you just made God's job easier. Now He doesn't have to look at the hearts or minds of creation. All He has to do is look at the labels.
Interesting that Paul didn't label them counterfeits,
1Cr 1:11 For it hath been declared unto me of you, my brethren, by them [which are of the house] of Chloe, that there are contentions among you. Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ. Is Christ divided?
He was just happy that Christ was preached,
Phl 1:18 What then? notwithstanding, every way, whether in pretence, or in truth, Christ is preached; and I therein do rejoice, yea, and will rejoice.