It is hard to believe that all this could be a PR stunt.
It would be exposed at once and bring ruin and disgrace to the perpetrators.

Not necessarily, not even probably. It's not at all hard to get away with this kind of thing, especially when the press is almost exclusively dependent on official sources, which is the case in Iraq at present. The one about Iraqi soldiers pulling babies out of incubators in Kuwait wasn't exposed for quite a long time. More often than not news stories get reported at the time, and never re-examined.

Is it logical to ASSUME that a reasonable claim is false, simply because the one making the claim is untrustworthy?

The logical thing in such a case is neither to believe nor disbelieve, until evidence emerges from a trustworthy source that makes it possible to decide.