I believe it's not the eggs so much as the oil. The egg is essentially covered in oil, keeping air from getting to it. Oil lasts a long time at room temp.
I know I've seen yellowed mayo used, restirred, in the past in my coffee shops and fast food. I've tasted it, too. It may have been just my imagination since I knew what I was tasting but it seemed that there was a great difference in taste. Not rancid, per se, more of a different texture in the taste if you know what I mean.