Not quite true, but what I have noticed is that, at the graduate-school level, there's a very low correlation between the quality of the program and the students.
If you go to a top-5 PhD program, you'll be surprised by how many of these supposedly "best in the generation" people just aren't that good. Many are, and the talented outnumber the talentless, but you'd expect there to be zero talentless schmucks at the top programs, and it just ain't so. This is where the OP's perception that PhD programs are "full of weak students" probably comes from; the fact that even top PhD programs can't keep the schmucks out. It's not hard, even for a total mediocrity, for a 22-year-old packing socioeconomic advantages, and already coming from an elite college, to appear smart.
Drop down to the #10 or #20 or even #35 department, and the talent distribution isn't much different. The difference, in raw intelligence, between the students isn't that strong. There are some really good students and some terrible ones, at any of them. The change is barely perceptible. You wouldn't be able to tell the difference except by the reputation of their advisors.
If you go in to a top school and expect its students to be the best of the best, you'll be disappointed when only 75-85% of them are halfway intelligent, and you might conclude that the #30 school has no intelligent students. In fact, it has almost as many. There are probably 20-100 times as many people (probably 3-5% of the general population) with the talent for academia as actually put themselves anywhere near contention for the positions.
What we now have, and it's not new, is evidence of a sorting system that doesn't really work. We can't sort talent from well-positioned mediocrity (read: socioeconomic status) before college, we certainly can't do it in college, and we don't do it for graduate school (George W. Bush is a Harvard Business School graduate). At all levels, we do a terrible job. We're actually talent-rich as a society, because we've had the smartest people coming here for generations. We just haven't a clue what to do with it.