I get what you are saying, but I don't think anti-intellectualism refers to people being against people who happen to have "intellect." And also, this claim about being a true intellectual seems like an impossible standard. It's possible to rigorously scrutinize an assumption drawn from smart types, sure, but nobody has the time to do that for everything that makes up their understanding of reality.

I could tell you right now that sidewinder rattlesnakes don't use their heat-sensitive facial pits to select thermally ideal ambush sites, they just use their eyes to pick a site that looks good. You could not deduce this without experimentation. (I was part of a study that tested it.)

Now, you could trust that I'm telling you the closest thing to the truth that is known in the world of rattlesnakes, but let's say you want to be intellectual by your definition and go know it without just taking my (admittedly qualified) word for it. You could go get a herpetology degree, go convince a grad student that it would be worth challenging our conclusion, and spend another three months like we did out in the desert catching snakes and running experiments with thermal cameras.

You probably don't want to do that, because you probably don't have the highly specific interest in snakes that we had, and so it would feel like a waste of your time. In the end, I think you'll probably admit that I know more about this snake topic than you, you'll accept my conclusion, and go around understanding it without having personally studied or observed it, and that's a good thing because it will free you up to go figure something out that fits into your interests and you can share your findings with me in turn.