I've seen some real-life examples that could be ambiguous, but technically they could be ambiguous even with the Oxford comma. One of the most popular ones I've seen lately is something like "Nelson Mandela, a dildo collector and an 800-year-old demigod." But even with the comma, you could still read it as "Nelson Mandela (who by the way is a dildo collector) and an 800-year-old demigod."
The problem for me isn't real ambiguity, but just a mental hiccup as I read. When you read a list, the inflection on each item goes up until the last one, which goes down. When I see a list without an Oxford comma, I tend to read it as "(my parents ↑), (Ayn Rand and God ↑) (oh wait that's the end of the list)". You have to be obtuse or uncooperative to think that the person really means that Ayn Rand and God are her parents. So it's not really ambiguous, but I feel like it's missing a little cue as to how it's to be parsed: "(my parents ↑), (Ayn Rand ↑), and (God ↓)".
That's why I like it and why I find arguments for omitting it to be less than compelling. Sure, I guess you don't strictly need it, but what does it hurt to include it?