It's possible to apply for grants without being in a university, though the bar to have your application taken seriously is admittedly higher. But, if you convince people you're legit, there are a good number of "businesses" whose revenue is mostly NSF grants, e.g. Cycorp: http://www.cyc.com/
Depending on your area, I'm not sure the overhead costs come out to less, though. If you're independent, you not only have to pay for the overhead of physical equipment out of that money, but also of a bunch of salaries and benefits (including your own, lab staff, etc.). You're also probably going to have to pay your researchers more than a university pays its grad students.
Depending on your area, I'm not sure the overhead costs come out to less, though. If you're independent, you not only have to pay for the overhead of physical equipment out of that money, but also of a bunch of salaries and benefits (including your own, lab staff, etc.). You're also probably going to have to pay your researchers more than a university pays its grad students.