From all your answers, I gather that there might be a AE-BrE difference here:
Some or Americans, or maybe all of them, generally pronounce "clothes" like "cloze". They do not do that "thingy" with the tongue FISH was talking about.
Britons pronounce "clothes", although they may transform it to "cloves", "clowes" or "clo-es" (akin to a glottal stop, maybe?). However, as "clothes" with its "th" is what they have in mind, they always "hear" a sound, even when American speakers drop the "th".
Converselly, an American speaker, used to his pronunciation, might hear "close" when a British speaker pronounces "clowes" or "clo-es".
Just an ad-hoc home-made hypothesis.