We still need more info from the OP about the toilet. Is the toilet positioned directly over the black tank? When pushing the pedal, in the past, can you look directly down the hole of the toilet and into the black tank? If so, what do you see now? Get a flashlight and look down. What do you see.
Is your toilet attached to a pipe that has a bend or a twist in it and not directly over the tank? If so, you could have a clog in the pipe, like what could happen in a house. But if the toilet is directly above the tank, I don't understand how you can have a blockage, unless the inside of the neck of the toilet itself is full. But pushing a broom handle down would have pushed anything in there on down. Otherwise, you have a poop pyramid from the bottom of the tank to the top of the tank.
Now, where that sewer water came from is very strange. Water runs down hill, unless under pressure. If your outside tank valves are left open all the time, and you have solid PVC type pipes plumbed directly into your camper tank, it's possible back pressure could potentially fill the black tank from the campground sewer system and back up into the bowel of the trailer. But that would have to be a LOT of back - up and a LOT of pressure to come out of the ground 4 to 6 feet high, fill a 40 or 50 gallon tank, and still have enough back flow to come up into the toilet bowl.
So the question we all need answered is, how is your toilet and the plumbing under it done? Straight shot down or through a pipe to the black tank?