If you were desparate to film on a roller coaster, this image tells you the procedure you are to follow to do so. Although this is mainly aimed at the media and press, I have known certain enthusiasts and YouTube channels be granted permission however it is a lot of hassle to go through but if you are serious....here's how to go for it. Least there'll say is no.
Like you say Zach, that link is aimed primarily at the press and media outlets.
In terms of regular guests being allowed to film on rides as and when they desire, that is not permitted.
I personally don't see the attraction of filming POV's. Except for the video quality depending on the device used, there's no difference between them all.
There are plenty of professional ones floating around on YouTube so, in my opinion, it's not worth the hassle of trying to get permission.