Check out Sheldon Brown's article about chains. Towards the bottom of the page, he explains how to measure stretch and what it means.

http://www.sheldonbrown.com/chains.html

Basically, if the stretch

a) less than 1/16" per 12", you have nothing to worry about
b) 1/16": chain is streched, but chances are, the cassette is fine
c) 1/8", cassette is probably damamged.

I'm not sure how to interpret the LBS's assessment of "quite a bit", but with a tape measure, you can easily quantify the stretch get a feel for serverity.