A question to a psychiatrist on delusions

Sorry, I'm not a psychiatrist. But I have been through therapy and hospitalization, so maybe my point is valid: Whether and how hard the psychiatrist presses depends on the delusion and the psychiatrist.
That is, if the delusion isn't one that suggests self-harm or harm to others, the psychiatrist may not press a suicidal patient for more details and roll with it.
On the other hand, I've had experiences with some pretty opinionated and/or pushy psychiatrists who would bear down on a patient no matter what (because they want to be proven right).

Not a psychiatrist but did a psychiatry rotation in Med School. Take the following with a grain or two of salt due to sample error.

Psychiatrists seem to operate in the mindset that everyone but them is crazy. I doubt one would care to investigate a patient's, "delusions." They will simply laugh it all off as delusional thinking and not lose any sleep over it.

This sounds like something a psychologist/counsellor/therapist would do, not a psychiatrist. Psychiatrists diagnose and prescribe treatment for mental illness, but don't do the treating. Nurses and pharmacists would administer the drugs (the former in a hospital setting the latter if the patient's at home) and someone trained in talking therapies (such as cognitive behaviour therapy) would be the one asking the questions about the delusions - generally to get to the reason why the patient believes the delusions and trying to address the incorrect belief at the root of them. However, it's unlikely that someone would get prescribed CBT over delusional beliefs unless there's other symptoms of mental illness there as well. People believe in all kinds of delusional things all the time and aren't mentally ill. If the person's having actual hallucinations related to their delusions - that's a lot more clinically significant.

A psychiatrist could be trained in how to deliver CBT and similar talking therapies of course, although it'd be fairly unusual.