All physicians are trained to do an H&P, but certainly many are pretty bad at it because they don't do it very often, if ever after their intern year.
The answer to your initial question is, not very competent. I don't think there are but a handful of psychiatrists that can do an appendectomy (and most were FMG surgeons that practiced over seas before coming here). Anesthesiologists do H&Ps every day as a part of their job and the vast majority of internists can not read MRIs at all (very few non-radiologists can really read MRI very well).