It's worse than that. It's selective and biased research... and sometimes they are unaware they are doing it. They don't ask the correct questions, in the correct way, to receive the correct answers.I've often found the folks that say "Do the research", or as you put it claim they've "done their research", are usually the least capable of actually doing the critical thinking needed in proper research and being able to sort out good information sources from bad.
1. They might make a false assumptions then ask something like "What percentage of the wealthy elite are lizard people?" or "Which democrats are accused of eating babies?"
2. It could be something less obvious like "What evidence is there to prove the Earth is flat?" The mistake here being that the search engine will ignore the evidence that the Earth is not flat.
Plenty of other examples, but basically, if you want to "prove" something, there is likely some "evidence". Furthermore, if you are insistent upon being "right" and have something to prove and argue about, you probably aren't going to search why you are wrong. However, this is exactly what we should be doing... hypothesis and null hypothesis.