My experience has been different. There are plenty of good, well-into-the 70's 4*'s who you can get before other schools start to take an interest. You won't get all of them, and some positions are easier to recruit than others, but you can get more than you should as a lowly mid-major.
I'm thinking about doing a test as UMass where I won't even add anyone to my board until week 4. I will add players only in the top 500 with low lock percentages, across all the positions, and see how successful I can be. Based on what I've seen so far, you might be surprised by how many of them I can get.