I read "do your own research" differently. I think it can go two different directions.

In the positive direction, it can mean "Ignore all the loudmouths, all the liars, all the self-anointed experts. Even ignore me, the speaker. Find out who really knows what they're talking about, and listen to them." This assumes, though, that the listener can do that. Am I actually capable to discern truth from lies, or even real expertise from incompetence, in virology? Maybe, if I devote enough time to it. Do I have that kind of time for every topic on which someone tells me "do your own research"? Probably not. So what it really turns into is finding someone who at least sounds like they are doing their own research (and doing it well), and listening to them.

More negatively, I suspect that "do your own research" at least sometimes is a veiled way of saying "If you really knew, then you would agree with me" in a much less in-your-face way than just saying it. The person saying this may have done their research as you say, finding a loud voice that said what they wanted to hear, and now be totally convinced that they are right, and that if you did your research, you would wind up agreeing with them.