Actually: if a foreign passport weren't acceptable as an ID, it would be impossible for citizens of a number of countries, Norway for instance, to travel on a domestic flight in the US, as the passport is the only govt' issue ID valid abroad, and for most countries it certainly is the only foreign ID recognized by the US Government!
Now when it comes to the competence of the "rent-a-cop-ID-checkers" in identifying a foreign passport as ID, it might be variable. But all foreign passports in the US should have some kind of US Govt' stamp in it: Visa Waiver entry stamp or Visa, so if the checker is in doubt s/he can look for that.
For what it's worth my NO Passport has been accepted as ID without trouble at ORD, EWR, IAD, TPA, ATL, PHX, EYW, FLL and SFO for domestic flights during the last year. Obviously these are all airports seeing a lot of foreigners travelling through: knowing that there are more official terrorist goals in Montana than in New York City, obviously I do not know how the checkers would react in suche high risk areas as Bozeman or Billings...