The Tiferes l’Moshe is clearly making this leniency dependent on which explanation you hold of. He writes that the Nafka Mina between chasnus and issur would be a mumar. If Bishul Akum is due to chasnus, a mumar is mutar. If it would be because of concern of treif, it would apply to the mumar as well.
The problem is that the Gemara and Shulchan Aruch clearly state that that the sole motive is chasnus. It seems that issur is only a hava amina, not even a dissenting opinion.