With regard to grounding:
If you are connected to a properly grounded pylon, you will be grounded (...and assuming you have a grounded electrical system in your camper ! ! ! ). BUT, always check what you are hooking up to, first! It is surprising how often I hook up to ungrounded (...or ineffectively grounded) commercial systems - - especially in the West were high ground resistance can foil the best of intentions. At least you will know that you are dealing with a bad ground and can inform the rest of your party to be cautious when handling electrical appliances.
If you are on a portable generator, you will NOT likely have a grounded system. GFCIs help in that case but are not a panacea - - caution must always be observed and everyone using the camper should be informed of the risks of handling power therein (...for example, don't use a hair dryer while standing in wet grass - duh!).
Contractor generators are meant to be grounded but this is not practical in a mobile camping situation. In practice, the results will be no different than if you are using an unbonded generator (...like a HONDA EU2000).
Electrocution is like the fifth leading cause of occupational death in the U.S. When you consider how many "experts" get killed by electricity, it is a wonder that we don't hear about more "amateurs" getting killed - - especially RVers and their 'homebrewed' systems.
Another albeit expensive solution is to put a power management device between your RV and your power source. A 30 amp Portable RV EMS device like that made by PROGRESSIVE DYNAMICS (they make a 50 amp version, too) runs about $270 on AMAZON and will detect a number of bad conditions (including the one in question) to protect you and your appliances. It WON'T CURE_ a situation like the case in point but it will protect you by shutting down the power until the problem is fixed.