FWNCR guidelines prohibit any fishing from shore within the park. I assume that cast netting would fall under that rule.
http://www.fwnaturecenter.org/guidelines/

I'm not going to pretend to know the laws on cast netting, but it sounds bogus. Why would a water body disallow cast nets from the bank but not from a boat. You could literally net the same exact areas from a yak. They probably had caught a few fish from there or had some kind of trap or lines around there, and didn't want a cast netter messing it up. People can get awful stingy with public property.
To make my point.
There is a lake that I used to fish working man tournaments every week at. Tournaments ran 6-10 on Monday nights. There was this one dock that seemed to out do the rest when it comes to flipping, and it almost always produces a fish or 2 worth talking about. Thing is, it fishes best right after sunset when the dock has the lights on. Any time the owner would notice somebody fishing his dock, he'd turn the lights off and on several times to scare off fish, then leave the light off. He'd even do it if he heard an outboard coming his way. You'd have to stop 6-7 docks down the way and fish to it real quick to avoid being seen. It was some real stealth ninja stuff. Anyways, point is, people will say stuff and do things to protect something that is public.

I'd take it with a grain of salt, but giving the local game warden a ring wouldn't hurt just to make sure you're okay.