Some sites may have thier own particular reason/H&S implications as to not allow petrol on site, period. but that would exclude the petrol driven engine.
As for the dangers in refilling a petrol engine on a diesel heated hot set up. I really don't se the problem, as the engine is very hot and you would't fill it when it was running (would you?)
I alays advice filling petrol engine up only when it's been stopped for 5 mis or more just to let the exhaust cool slightly. So we always top up just after a brew before restarting again, even if it only needs a couple of litres