The moment they heard my accent, they immediately told me the place "was full" and that I'd have to go 1.5 miles to the next beach. As I was exiting, I saw them allow at least 4-5 other cars in after me. Guess there was enough parking for "locals"? Don't know what's going on there, tbh.
Update:
Just walked in here from the other beach side, and there's tons of parking! The photo here is just one of many vacant places.