I did not see the show in question. However, I live in the southeastern US and the local, native pronunciation of that word would indeed be "swimmin" with no trace of a G.
Even though standard American pronunciation and grammar are taught in the public schools, there are still many natives who talk in the local dialect. So I can believe that this woman would pronounce it "swimmin" in her daily life, off-TV.
To me, the question would be whether the contestants were given instructions ahead of time that answers must be in standard American English pronunciation. If they were warned, then I suppose she took the risk.