Anything is at least theoretically possible, including Bev holding engineering degrees. What I said was that we have no reason to believe it's true. We've never seen her so much as repair a toaster (or the 24th-century equivalent thereof). Her off-duty interests seem to run more to the arts, like dancing and theater. She also experiments with growing alien plants, so we can infer an interest in botany. If we're supposed to believe she's interested in engineering, shouldn't we have seen at least a couple of little hobbyist motors in her quarters? Or at the very least, some tinkertoys?
Yes, Beverly
is an extremely intelligent woman. We don't have to guess that -- we've seen the proof! She's a top-ranked doctor, and she even was called on to serve a stint as head of Starfleet Medical. You don't get to be head of Starfleet Medical without having major brains. But having major brains doesn't make you an expert in engineering, either. My best friend has an IQ of 130, which is pretty darned intelligent by most standards, but she couldn't repair her radio if it broke. She has the brains, but she doesn't have the specialized knowledge.
Actually, the fact that Bev
is such a darned good 24th-century doctor argues
against her having a lot of knowledge about engineering. As technology advances, fields of expertise tend to become a lot more specialized. Look at all that a good 21st-century doctor has to know, compared to what his or her 18th-century counterpart had to know. Ditto for a 21st-century engineer compared to his or her 18th-century counterpart. Bev is another three centuries into the future, with all the additional knowledge that implies -- not to mention her specialized knowledge of the biology and medical needs of many non-human species! You're suggesting that with all that she has time to take a doctorate (or know as much as a Doctor of Engineering) in a subject where she has, at most, a passing interest?

Not very likely, to say the least.
Which brings me back to an earlier question, which is, just how
did she end up hosting that engineering conference where she learned so much about metaphasic shielding? I've always wondered if "Suspicions" wasn't originally supposed to be a Geordi episode, and then maybe Gates McFadden complained, "Hey, I haven't had an episode all season!" Or something like that.
As for Picard, it's true that he never went to a tech school, much less a College of Engineering. But we trust his
command decisions because, as a captain, he's a trained tactician, and he knows the capabilities of his ship. Bev doesn't have that kind of day-to-day working knowledge. One could actually argue that Picard handicapped Bev in this episode because he took the Chief Engineer planetside, where Bev couldn't draw on his expertise -- but it actually makes sense for Geordi to be planetside in this case, because he has more influence over Data than anyone else. So it was
lucky that what engineering knowledge Bev had, improbably, acquired was actually something that could serve her.
Very lucky.
And I still say that it was reckless and foolish of Picard, in this situation, to leave his ship in the command of anyone other that a trained and experienced captain. As VOY's "Workforce" demonstrated, there is a great deal more to starship command than simply being able to pass a test. If you're not familiar with that ep, I'll explain the pertinent part: the holographic doctor, having downloaded a database of command knowledge into himself, assumed command of the ship in the absence of other senior officers. He quickly learned that knowledge wasn't all he needed to be able to do the job.
Picard's ship was in a highly dangerous situation, sitting in the territory of the most dangerous foe the Federation had. In the best interests of the
Enterprise and her crew, the most capable -- most command-trained, most command-experienced -- officer should have been in command. For some silly reason, I think that would be the guy who actually was captain. But any way you slice it, it sure wasn't Beverly Crusher.
Brennyren