I think that by using the term "Free WI-FI", the campgrounds are giving themselves an easy way out of guaranteeing you a good connection. By saying it is free and not a part of the paid-for amenities, they can tell you "it's free and not included in your expenses, so if it doesn't work, oh well. What do you expect for nothing?"
I use Verizon Wireless for my MIFI and I have AT&T for my iPad which I can use as a wireless hotspot if I need to. I have yet to visit a campground that I can't get at least one of these carriers.
Bruce