These people would still ask and waste your time without AI. The fact is, they don't even bother trying to find an answer themselves. And it's often something Claude is extremely good at finding out. Which is why my first suggestion was if you used Claude, then let the person asking know that it worked well for you and encourage them to use it. It's their own competency at their job to judge the output, they shouldn't be pushing the hard bit onto someone else.
If someone uses AI or some other research and then comes to you with their findings and other questions then that is infinitely better to me. I absolutely despise people asking me basic questions that involve me literally doing the research job for them.
If they come to me like "Hey, I have X problem, I used Claude like you suggested and it came out with this response. I'm not 100% sure it's correct because of Y. Would you be able to take a quick glance to see if it's on the right track?". I am much happier with this question because it's clear they have actually tried to research themselves.
Ignoring someone who doesn't even do the most basic research is 100% a defensible position. People should be doing their job.