Key phrase: NO static.
And no an AM radio may well NOT need a good ground plane.. And I can prove it if anyone wishes to argue.
I do not know your radio but I suspect a problem internal.. However a visual inspection may show something. IF this is a DASH radio.. Many RV's have very short Dash Radio antennas.. They really do not work well for AM (Do not work well for FM but they REALLY do not work well for AM) Make sure the antenna connection is well plugged in.
Now I can improve the AM antenna on an RV, but frankly not worth it (in my case) Since I have a nice ham rig that covers the AM (General coverage receiver0 and I have a nice LONG!!!!!!! wire I can toss up when parked.
Am Broadcast is the 300 meeter band, this means a quareter wave (Ground plane needed) is 75 meters long.. a 1/2 wave (NGP) is `150 meters long.. A meter is a bit more than a yard.. That is a LOT of antenna.. Anything shorter is a comprimise.