Oiling bike frame to keep it cleaner?
I'd think that oil would repel water (make washing harder) and attract dirt. Maybe since we're in such a wet climate (Andrew and I live near each other) it's decent advice to keep the rain/wet trails/dirt of your bike but I still think that your bike would gather dirt even in the West Coast rain. Especially in areas that are hard to get at like around the seat stays and seat tube.

We oil our chains and they get filthy, even on the road. I'm not sure why it would be any different with the frame.

I can't see any scenario where that is good advice. I agree with the comment that waxing would be a better option.