How incorrect in portraying my position.

DWA: As a preteen, I myself discovered that there is indeed a stalemate in checkers, and later, in chess. That is, unless the successful barricading king/last movable checker voluntarily steps out, under the established rules, to meet the sword, or run, run, run, to a new square. :-)

It is true that one can get a stalemate by having only one piece and being unable to move. In this case, having all the available evidence going against your beliefs but refusing to admit it is indeed a stalemate, but doesn't really qualify as a draw. Keeping your fingers in your ears and screaming, "I can't hear you!" may keep the noise out, but it doesn't mean that the sound isn't there.