It's as you said "Private Property" so they can set the rules as they desire..but even if it was Public Property you would need to have a Signed Property release (similar to a Model Release) if you wanted to use the Images for Promotion of your Photography or to sell to s Stock agency. It's just the way it is .
They do have a photography Permission form right on their website though. But that would only give you permission to photograph there. Not use permission.
If you are on a Public Area, Streets, sidewalk you don't need permission to shoot, except certain Government Area's and Buildings But even with that, Your "Use" may be limited without a Property Release. i.e. you can take as many shots as you want at Disneyland, you just can't sell any.