Hi ClockDrFla,
Not much experience with RV electrics, but some with electricity in general, so I will try to help.
"Open ground" means discontinuity between the ground wire arriving at the surge protector and the Earth (which behaves as a large electrical "sink" where excess current can be dumped in case of malfunctions to protect the user, etc), so it's something important that you should investigate and fix.
Whether it's the CG pedestal or your cord or even the surge protector itself depends on many factors.
It would help knowing the brand/model of your SP, as Jatrax has asked. But, if it's a "dog bone" model and you are connecting it directly to the pedestal, then the cord cannot AFAIK be the culprit.
It could be the pedestal, even many of them at the same campground, because often CGs have wiring errors throughout their installations, and because often all the pedestals have their grounds wired to a single grounding rod whose connection, or even the rod itself, can be corroded. Oftentimes the CG just keeps chugging along with those faults because many (most?) customers have no SPs or have them but ignore their warnings.
There's a procedure for testing the ground pin on a wall plug using a multimeter and a light bulb in a lamp socket, but it's somewhat involved and if you are not comfortable with electricity in general, it's not something I'd suggest that you try.
Some SPs have a self-test procedure, which usually runs automatically when you plug it, so you.might try to observe it (check the SP manual).
You could also try complaining with the CG people and see what they say (perhaps they are aware of the problem and will tell you so), or you could also call your SP manufacturer and ask for support.
Good luck and please keep us posted.
--
Vall.