Further on that point: Chambers gives as one meaning of "to wear" "to consume, waste or damage by use , time or exposure". This equates with "rubbing away" but not with "putting on the outside"!
Do you mean the 12th Edition, Mamyalynne? It's certainly not in the 11th. And even if that is so, I must say for me it still doesn't make sense. Does it make sense to you?
Sorry but people are talking rubbish here! I am a crossword compiler and know what 'wearing' indicates. If you wear something you are inside it; it is NOT inside you. The compiler has made a mistake.