If gone for more than a week or two I'd be pulling all the food out of my refrigerator. Saw a news report just recently where a representative from the CDC was going over some food precautions for the July 4 "Weekend".
Leftovers put in a refrigerator should be consumed within 7 days or discarded. Packaged food that requires refrigeration has varying "Use by or best by" dates but can spoil quickly if the power fails for any length of time.
Frozen foods should not be re-frozen if they thaw due to a power outage.
Unless it's something that's inherently safe, like a jar of pickles, Ketchup, Mustard, etc, I'd be loading it up in a cooler and taking it home. Would also turn off the Refrigerator while gone.
FWIW, state laws vary but in our state if you sell something to customers that is "measured", like gasoline from pumps, produce by weight, etc, the "device" used to measure has to be regularly certified. Power companies regularly change out meters so they can be re-certified but chances are the power meters in campgrounds are owned by the campground and the power company just charges based on a single meter coming into the campground.
The person experiencing the high bill should make a formal complaint (that means in writing) to the campground and if they fail to take action (like having the meter tested) then move to the next level, usually a state's consumer protection division of their AG's office.
If nobody has a Kill-a-Watt meter, just plug in a hot plate or heater that draws a known amount of power. Start a timer when it's turned on and run it for an hour. Read meter before start and at end. See if there's an error.
From what I read it should be easy to see how much the error is and after converting it to a percentage, see if it coincides with the percentage the bill is greater than others.