I've deleted my previous patch, as I found the code working as intended.

The domain_specified signals whether the domain stores came from a Domain: tag inside a Set-Cookie request or is taken from the hostname of the request.

The rfc2965 dictates that a value taken from a Domain: tag should be
prepended with a "." if the values doesn't include it. Once stored in a LWPCookieJar the same logic is used to signal if the domain_specified is true or false. Thus the observed behaviour.

The LWP-Cookies-2.0 format is an extension to the perl format, that seeks compatibility adding some features.

About the domain matching, the rfc2965 documents this. I think the perl comment is an example for a.b.c.net, so that matchs with .b.c.net but not with b.c.net.