That seems like an extreme interpretation if I'm honest. As ever, its more likely somewhere in between your hammer analogy and the handyman. In any case, there is almost zero downside to listing your sources when answering a question as it provides the person asking the question with more context as to the origin of the answer
If you provide sources, provide the sources the LLM found for you after checking them yourself. Otherwise the recipient will have to vet them.
Slight rant: I’ve started to get a bit fed up with people antrhopomorphizing these things, it’s unhealthy. It’s definitely not a handyman and it really is just a tool. I know they’re designed to seem conscious and that just makes them dangerous to use. If my colleague starts treating his hammer as a person, it’s definitely not normal.
Does your handyman go off the rails and build pipes around the neighbors house because they didn’t know you already have an incoming water pipe?
Does your handyman require you to have expertise in plumbing to make sure they don’t use bubble gum to seal the pipes?
It’s not taking credit if the “handyman” is a gibbering idiot who needs more handholding than a child.