Is this rule "common"? Probably not. I've not seen such a thing, nor have I read anywhere else of such a rule.
It would actually raise a red flag for me, and likely others. Why would they have such a "rule"? How are they going to know if you're using your electric heater inside your rig? (A/C would make noise, but not a heater inside). This would seem to indicate they have some sort of issue they are not disclosing, with their electrical system.
Only way to know the answer(s) would be to ask them. Call and ask why this is a rule, and see what their response is. That way you, and others if you post their response here, can make an informed decision.