Those are earwigs, mostly a nuisance pest but sort of spooky looking. They may be responsible for eating the basil but there's a good chance they just happen to be in the wrong place at the wrong time and are taking the blame for something else.

Here's a fact sheet about earwigs:
 http://extension.colostate.edu/topic-areas/insects/european-earwigs-5-533/

For a better diagnosis on the basil, you should bring in a sample so someone can take a look. The Denver office is at 888 E. Iliff Ave. (north of Porter Hospital, in Harvard Gulch park). Call first to make sure someone is available:<personal data hidden>.