I heard this sentence in an American film a while ago as I was watching it on DVD (the part after but is verbatim):
"I'm doing my best but I mustn't be doing it right."
This is something I occasionally hear in American films: phrases like "he mustn't have done it" or "she mustn't be studying now", where a logical conclusion is expressed. So far I've thought that the normal thing to say is "he can't have done it" or "she can't be studying now".
My question is: Can mustn't be used to express a logical conclusion when the speaker is certain that something didn't happen or isn't happening, at least in informal speech? Is this an American usage? (I've never heard this usage in British English, but this doesn't mean it doesn't exist.) Is there a change going on in the usage of the particular modal verb?
Note: All the references I've checked don't even mention this use of mustn't. Google books aren't of help either.
EDIT: I should clarify that I'm asking this question because if I wanted to express that I'm certain I'm not doing something right (as in the sentence quoted from the film) I'd say "I'm doing my best but I can't be doing it right". I would think that the use of mustn't/must not wouldn't be standard usage (although the meaning is perfectly clear to me; I never mistook it for an injuction).