Yes and no.
Yes in the sense that it's ultimately you who will get fucked up; you'll be the victim, you're the one punished for the mistakes of others.
And no in the sense that the social contract says different -- otherwise, you'd be responsible for baking your own bread AND manufacturing and fixing your car AND writing your own computer & smartphone programs AND taking care of your health AND educating your children AND cultivating your land and growing your own produce AND so on and on. We have "distribution of work" for a reason; you take the money, you take responsibility. (Except most doctors.)
So, "no", it's not your job, but "yes", you're held accountable for it.
Just because the social contract gets violated left and right, the violations aren't right.
People always emphasize that responsibility and authority should go hand in hand, and this is a prime example where that principle is shown invalid -- it's a human construction and does not hold up in nature. You have no authority to even understand your own health sufficiently, yet you get to bear the consequences.
What you are arguing for is that everyone should judge a professional from a position of lacking education / information. That's precisely what the social contract is not. I'm not saying you are wrong, I'm saying the state of the world is fundamentally wrong; it's way too easy to disclaim responsibility. Someone takes my money, they're on the hook.
People shouldn't trust the social contract, but you can't blame them for trusting it. Most of the time there's no way around trusting it.
Case in point - just last month: To bring my LDL further down, I was prescribed a doubling of my existing statin dosage. I checked with an LLM and it turns out it's a crap idea, as doubling only weakly increases the effect, while the unwanted impacts on the body increase. Supplementing the existing dosage with bempedoic acid or Ezetimbe would be a way better strategy. I brought this up with the doctor, who immediately agreed it's a better idea and changed my prescription.
It's your body, your health, your future, your loved ones, your home, your career, your investment, your savings. If you care, check the work, the tools exist and are now ridiculously accessible.
Well I certainly have an excuse: at work, code reviews provided by a particular LLM have been a net negative contribution, in my judgement. And then it's not hard to extrapolate that experience to other professions, ones that I myself am not competent in.
The old adage exists where you read the Sunday newspaper, get a nice educative experience from 14 out of the 16 pages, but then 2 pages happen to write about your own profession, and you seethe about the rampant stupidities and mischaracterizations in those 2 pages. But the other 14, about stuff you are not directly familar with, sound good. See the problem?
You got lucky because your doctor was receptive to ideas from sources other than his own brain (LLM or otherwise). Most medical professionals laugh you (or curse you) out of the room, if you attempt to make an informed decision. In fact the most selective search criterion for doctors, as a patient, is willing to talk.
If you care about something, take in interest in it and learn to advocate for it. Don't conflate handing someone money with making them care about you.
Do also remember though that more people are struggling than you probably realize. That includes the people you are paying. The world is not easy right now, but it rarely has been. I'm not religious, but the concept of grace does have an appeal.
Ultimately, I find thinking macro helps. Realizing it often doesn't matter or would create an unnecessary trade off can help. Advocate. But pick your battles. More and more of us are running on empty, part of taking care of yourself is learning what to care about and what to let go.
Most don't realize that "Meritocracy" was coined and popularized as a slur and was meant to be a dystopian concept.
The other problem is that when you do try to engage with those professionals in technical terms, most are utterly unable or unwilling to communicate with you on that level. Trying to actually get the "informed" part of informed consent makes the level of revealed incompetence jump from maybe ~50% to 90%. Only very rarely do I find a doctor (or really any professional) willing to get technical, even as they ask me for approval about technical decisions!
The fundamental dynamic, as always, is they want to claim authority while disclaiming responsibility.