Yes they do unless you specify different, navigate in the team site  to your doc lib.

Select Modify settings and columns

Under general settings click change permissions  for this document  library

You should not see the groups listed change as required.

All Lists/Libraries in a WSS Team site  inherit their rights from the
site unless you specify that the List/Library has a different set of
rights (the reverse of your statement below). That is list rights trump
site rights.

When you specify unique rights for a given list, you can specify
anything that you want regardless of what is defined for a Site. For
instance, you can give  an individual or group that doesn't even have
access to the site read, write, or even manage rights to that particular
list (people with access to a list but not the site are in the built-in
Guest Site Group). Oddly enough, you can give a Site Group, like
"Readers" any kind of rights to the list. So, for instance, you could
say that people associated with the "Contributors" Site Group at the
site level only have view rights on the list/library. Or you could say
that people associated with the "Contributors" Site Group at the site
level have manage+ rights on the list/library. It's kind of weird to
think about it.

Note, Site Administrators, Site Collection Administrators, Virtual
Server Owners, Farm Administrators, and people in the Web Server
Administrators group will all have cart-blanch access to all rights
defined in the rights mask for a Virtual Server regardless of whether
they are explicitly listed or not.

SharePoint List Sync shares and syncs documents, files among collaborators as well as set permissions to specific users. http://www.sharepointboost.com/list-sync.html