National Parks - ReserveAmerica shows full - accurate?

OP, national forest campgrounds typically don't have reservations on all the sites. When you look at the reservation site you should see a N/A (not available) symbol on some of the site. This means they are first come sites. It doesn't mean they are taken.

What park are you looking at? Perhaps I can look it up for you to double check the symbols.

However, there could indeed be instances that everything is reserved. It's still summer travel.