R’ Moshe says l’hedya that it’s not yuhara to be machmir.
I believe that in at least one of the teshuvos he just says raui l’hachmir without mentioning baal nefesh.
Certainly, in that famous letter to R’ Weinfeld, he says it’s not l’chatchilah.
So your mesorah (or how you’re applying it here) is wrong.