Yes, that matches well my experience with NSF (in astrophysics).
Most goes to the University in overheads + grad student + (maybe) postdoc, and a little bit to cover your summer salary (which is an insane concept if you ask me).
There is a reason university administrative overhead has exploded over the past few decades: MBAs have found yet another vein of money to parasite themselves onto. I think this country will only start to get better when 90% of this management overhead is fired and forbidden to work in management ever again.
>> a little bit to cover your summer salary (which is an insane concept if you ask me).
It's a brilliant concept though if you look at it another way.
Imagine the university has $120k per year allocated to your salary. Is it better for them to pay you 10k a month for 12 months, or 20k a month for 6 months?
You're seeing this as "they should pay you 20k a month for 12 months", but that option is not on the table (your post pays 120k).
By paying you 120k over say 9 months, they set your-value- at 160k. So you're free to get extra grant money, consulting gigs, whatever. For grant purposes they're capping your income at 160k,not 120k.