If they put rubbish in without your permission it's fly tipping and illegal. As the skip hirer you are responsible for the waste that goes in it and if anything dodgy goes in it comes back on you.
I've dealt with a few skip companies over the years, some are stricter than others. I've got a permanent hire at the moment, I just call them when it's full to get it swapped. It's hired as general waste (new house building).
Some of them are really strict about what goes in, even if you book it as "general waste", there are strict environmental rules about what can go in it.
If you've booked it as building waste, rubble, bricks, tiles etc, best not to put anything else in it. That is usually recycled in to type 1 MOT. You could face a charge back for contamination.
Best to check what the T&C's are if you're gonna let anyone else put stuff in it.