This answer misses the point. The handy rule you've been taught — we've all been taught that handy rule. We all know that "my wife's and my" is Standard English; we all know that a stanalone "I's" is not; but this question is about neither. It's about a peculiar construction produced by a native speaker (who himself is well aware that it's non-standard) and an attempt by another native speaker at an explanation of why it was possible for it to be produced in the first place. This question is all about putting that explanation to test, and the top and accepted answer adequately does just that. —
RegDwighт 2 mins ago