I agree. One critic at the time, and I don't recall who it was, described Marvin's rendition as eloquent and perfectly in keeping with his character. Ben Rumson was not a Met star or a Broadway musical actor...he was a rough, under-educated and flawed man.
My favorite two moments in the film are the simply beautiful "A Million Miles Away Behind the Door" and Lee Marvin's touching rendition of "Wand'rin Star". Both those songs captured moments that the rest of the film should have aspired to match, but didn't.