base doesn't enter into it; all use base does (handwaving slightly here) is use the named module and diddle the using module's @ISA. Since Net::DAV::Server doesn't use Exporter and has no special import sub of its own doing anything similar, nothing (underscore or no) gets imported into the using module's namespace.

Update: I just re-read your last paragraph of your original question and I think I see what you're misunderstanding:

Perl inheritance (what base sets up) only affects method calls, not subroutine calls. Since the call is made as a normal subroutine call and not as a method call on an instance inheritance and @ISA never enters the picture.

That clear anything up?