The cheshbon is that techeiles and tzitzis are two separate mitzvos. Tzitzis is a mitzva on the begged, tcheiles is a mitzva on the tzitzis. (according to RaMBaM, RAAVaD says they are one mitzva). We are putting ourselves in a position to be mechuyav in tzitzis out of chavivus, but — if we don’t “hold of” Radziner or murex tcheles — we are onsim on the second mitzva and can wear arba kanfos without a problem.
Incidentally, RaMBaM is in the minority when he says that the wrong tcheles passuls the tzitzis. By all rights Brisk should wear a Rabbeinu Tam k’shira with one thread being Radziner tcheles and the other being murex to be yotze kol hadeios.