As for Greek potamos, I’ve checked in Dictionnaire-Etymologique-Grec : Chantraine (It’s online?! Download while you can!!!)
Its likeliest source is as a noun derived from e-pet-on “to fall” (so, waterfall, torrent); but the meaning means that rivers always fall, which doesn’t sound right. The alternative derivation given, proposed by Wackernagel, is a relation to German Faden “embrace” (which would indeed go back to Proto-Indo-European pot-). More detail in Frisk’s etymological dictionary.
No, I don’t know how “embrace” is more plausible than “waterfall”.
EDIT: Frisk’s dictionary is at the same place. (For now.)
Oh! Faden “embrace” is related to the Greek verb pet-annumi, and its noun petasma, “spread, broadening”. So “something that gets wider”. Ok. And the Old English parallel is flōdes fœðm, “spread of the flood”?
Derivations Frisk rejects: potamos < *topamos, cf. Lithuanian tekù “to run”; and some guy who inevitably said “I dunno, therefore Pelasgian”.