I'd be interested to see the data for unis showing their costs are lower. I doubt it.

For private companies, and an SBIR ,you have to establish an indirect rate based on your actual costs. The rate is the ratio of all indirect costs for the company vs the direct costs for the project (salary times the % of the person's time). It's a bit of work the first time you have to do it.

I'd be surprised if the NSF lets the uni just put whatever they want down and it isn't based on submitted budget data.