I don't have recruitment data so its quite possible those companies recruit far more heavily from those schools, but even from my own anecdotal experience at a

I don't have recruitment data so its quite possible those companies recruit far more heavily from those schools, but even from my own anecdotal experience at a top 30 (yes 3-0) state school in CS I was still getting recruited and interviewed by Amazon, Google, and Microsoft. And that was as a Physics major with only a CS minor in my Junior year. I doubt getting interviews with those companies is the issue, they are ALWAYS looking for more talent wherever they can get it.