But it doesn't sound anything like insect damage! It would be equally logical to spray with a fungicide for good measure while you're at it.

It's almost certainly the result of someone spilling something on the leaves, and the aviation fuel theory sounds the most likely. Not something I'd ever heard of, so good to know about it.

The wiping off with wet finger suggests the best thing to do would be to chuck a bucket of soapy water over the whole lot and try to get rid of the stuff before it can do any damage.