The Teimanim followed the Rambam’s Psak from way back when. The developements of Ashkenazic and Sfardic Halacha didn’t change them all the way. However, this has nothing to do with being Choleq Al Rabbo.
In Yiddish we say, Fuhn Ah Kasha Shtarbt Mehn Nischt. If you want to think up reasons for each place where the Rambam seems to go with outside Sefarim, or if you want to come up with general ideas, so be it. This is something else entirely.