For those who doubted that good grooming and kinky food fetish play could go together, there's your proof.
Honestly, it sounds like a prank. Wasn't there a whole Simpsons subplot about this going disastrously wrong?
It seems like such a nonsense answer because, well, gum is sticky, and peanut butter is sticky, so how would this not just create a bigger, stickier mess? And one that makes it look like somebody took a shit on your head? The secret, though, is the oil.
Meaning if there's no PB&J around, you could probably improvise.
Basically, the reason gum doesn't come out with a quick shower is that it's a hydrophobic substance -- it doesn't dissolve in water. Try to wash that shit out and it will only stick harder, like an alien facehugger poked with a scalpel. But it does dissolve in oil, and peanut butter is full of it.
"Wait, doesn't that mean I could use cooking oil or some shit instead?" Sure, and you can browse YouTube and watch thousands of videos of people using olive oil -- it seems to work fine. People always cite peanut butter either because it's easier to work with (as opposed to leaning over the sink and dumping half a bottle of canola oil on your head) or because it makes a more interesting "fun fact" since it's so unexpected. Hell, that's why we did it.