It's not just Federal lands.
I do some hi-def wildlife filming, and I have an underwater case.
I went to video some Manatees at a state park here, and you would have thought I took a gun to hunt them. The rangers were very heavy in their questioning to assure that I wasn't engaged in commercially filming them. I responded that I knew the rules, including staying at least fifty feet from the manatees, but I explained with zoom and the clarity of the water that was no problem.
They then closed the swimming area down completely.
It's bad enough that I pay 80.00 a year to access the state parks. But if you do want to film commercially on the state parks, you must negotiate the fee with the head ranger at each park. - state sponsored capitalism - ( or good ol boy network) - you choose.