The 8 times I was talking about was specifically the presidential election. Moreover not only did a third party win, but in every case except for one the third party became the new majority party and the majority party that lost went out of existance. So 8 times.
The fact that it hasnt happened recently should tell you that it has nothing to do with FPTP (since we had that for our whole history and had 8 transitions) but rather something more recent to blame.