Did you ever find out the answer? It seems more of a riddle then an ME question. Even if you could add the heat due to friction, just plain olive oil couldn't heat up enough from friction to burn someone, well not from the height that it would drop. Also he never gave you the height of the eater there for obviously it had nothing to do with how far it travels.

I mean olive oil can burn, well be used for lamps and such, but you'd have to get it pretty hot. So I guess it's pretty easy to prove it's not possible, oils burn around something like ~350'C so you could say that in order for the oil to burn, it would have been at temps much higher then to cause a burn also it would have been on fire unlike a boiling drop of water.