If it is a busy park I guess they are not too worried about you being a no-show. Somebody else will roll in to take your place.
In another life but in a similar situation to a CG I would take the card to be sure that somebody did NOT pull a last minute no-show on me after I had turned others away. Been there. Had that happen lots of times by inconsiderate people. When you have their card people tend to remember where they are supposed to be & when they are supposed to be there.
With CGs there have been many who do not take a CC# on reservation. If they have lots of space they will not lose if there is a no-show. The site would be empty anyway.
With the exception of busy holiday weekends we don't make advance reservations any further than a couple hours out or maybe the day before. Works for us.