modal verbs - Can "mustn't" be used for conclusions?

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).

Answer

Per my comment, I'd avoid it because it sounds rather dated and "upper class" to me.

Semantically, the reason for avoiding this construction is simply that it takes the focus off the critical word not. Since the "conclusion" clause is intended to convey something along the lines of "I am failing", this negating word is vital to the sense.

In "injunctive" forms, such as "You must/mustn't do that!", the word must is invariably stressed, to emphasise the intended meaning. In OP's usage, the word must wouldn't normally be stressed, because there's no sense of injunction or stricture (except loosely, in the sense that there's a logically enforced conclusion). It's "not doing it right" that counts, which requires not to be vocalised.

To confirm this particular contraction is nonstandard, note just 3 instances of "I mustn't be doing" in Google Books, but 3830 for "I must not be doing" (almost all for the sense relevant here).