The extreme low power at which a MiFi operates is not going to interfere with the campground WiFi system. Period. If you take your MiFi into the coach next door and the stars are all aligned correctly, you might be able to cause an issue with that campers connection but it still would not effect that parks connection in any way.
I use a WiFi Ranger in my RV which puts out a pretty strong signal but I can still use my own router or the parks router to connect my computer to the internet without issue. It's truly just a campground either trying to make excuses for their crappy system or the person who wrote it had no idea what they were talking about.
If any of it were true, none of us would ever be able to get on the internet! How many times have you pulled up your WiFi connection page only to find 20+ connections available? With an external antenna I have pulled up as many as 50 available networks without any of them causing any issues.