Try these:

1. Remove full permissions on that file - it's very bad.
2. Set the user that runs squid as the owner of the log file and set the permissions to 0640.
3. Set the group that owns the log file to whoever you want to be able to read the file.

Then try these tests (stop when you find the problem, they get more fiddly as you go down the list)

1. Double-check your config file.
2. Switch user to the one running squid and try to write something into the file (echo "test" > /full/pah/to/config.file)
3. use lsof to look for the filehandles the running process has open, find where it thinks it should be logging to.