As far as diaper changes in the hospital go, BM and urinary output get charted, and if you are wearing a diaper but aren't incontinent, yes they are going to ask you awkward questions. Charting requirements vary from hospital to hospital, but some will add it to your record if you are diapered, and if you show up in a diaper but denying incontinence, don't be surprised if you are given a psychiatric consult. If you are incontinent, and are alert and oriented you can refuse a catheter. Usually a CNA will assist in changing anyone who cannot change themselves, which is most incontinent patients in a hospital. For those of you with nurse/doctor fantasies, please keep it to yourself while in any healthcare setting.
In the emergency department, if a patient is somewhat incapacitated but can be assisted using a urinal or bedpan, that is usually what they'll do. If they're not alert, intoxicated, require immobilization, etc, they'll probably receive an indwelling catheter. More or less anything appropriate goes for drunk or otherwise incapacitated people, under the doctrine of implied consent, and a catheter is usually considered appropriate.