Etymology of two rockin' senses of the word "cover"?

This has the ring of truth. I intend to start believing that this is the origin. (All due apologies to them as think differ’nt—you might be right, but I can’t pretend matt_mcl hasn’t persuaded me, cause I’m persuaded.)

The only thing I would question about this theory is a lack of historic cites. The Wikipedia cite is of little use.

If I understood **matt_mcl **correctly, there are restaurants in Italy today that charge something extra. Can you give me any information that this was true of Italian restaurants in the 1900-1930 period?