The verb to question means different things, depending on its object. To question a person is to ask that person questions, usually in the course of an investigation or a trial. To question almost anything else is to raise questions, that is, doubts, about that thing.
The latter sense of to question can, of course, apply only to things that may be questionable. Nobody of sound mind is likely to say,
I question the refrigerator.
We might, on the other hand, question the existence of the refrigerator, or the need for the refrigerator, or the suitability (or any other purported attribute) of the refrigerator. In which case, of course, the object of the verb to question is not refrigerator, but existence, need, suitability, or what have you. In this sense, a refrigerator is not, and cannot be, questionable.
One can, of course, talk about “a questionable refrigerator”, but then, strictly speaking, what is questionable is not really the refrigerator, but some quality thereof, such as, perhaps, its cleanliness.
What are we to make, then, of the following sentence, taken from an e-mail exchange concerning reports provided by a financial adviser to a client?
I have questioned the possibility of eliminating the hard copies and they said I should communicate the matter with Mr. [Tompkins] who is heading the portfolio.
To question the possibility of something usually means to suggest that it is not possible; but that’s not what this writer means. She or he has in fact raised the possibility of eliminating hard copies, presumably by asking a question about it.
I strongly suspect, also, that he or she was not told to communicate the matter with Mr. Tompkins.
I suspect that this sentence is merely an example of what I’ll call officialese (of which announcementese, which I’ve mentioned before, is one variety), the bizarre language of people who deliver official announcements, instructions, and, as here, business communications that may be read by their superiors. Somehow, communicate strikes this writer as more business-like than, say, discuss or take up, even though in ordinary English one cannot communicate a matter with somebody. Apparently, it is better to sound illiterate than informal.