Actually --list-sigs is more of a debug command than a command users
should use to verify a key.  The real command is --check-sigs and it
does what you suggested. 

Unfortunately the man pages describes --list-sigs in detail and only in
the next paragraph --check-sigs is explained in terms of --list-sigs.
it might be better to merge them into one description with a focus on
--check-sigs.

Or just describe --check-sigs and have --list-sigs tucked away in an
"experts only, beware" section.