Ok.. I just had a play with 2 Site Collections in the same web app.
http://teamsites/teams/Site1
http://teamsites/teams/Site2
I set both to have the Document ID Prefix: "TEST"
I Uploaded a file to a Document Library in the root web of each site Collection. Both got a "friendly" Document ID: "TEST-1-1"
The URL associated with these Document IDs are under the Site Name:
http://teamsites/teams/Site1/_layouts/DocIdRedir.aspx?ID=TEST-1-1
http://teamsites/teams/Site2/_layouts/DocIdRedir.aspx?ID=TEST-1-1
So DocumentIDs are completely contained within the Site Collection, however, you can link to another document by it's ID by putting in the correct full URL.
This doesn't help so much then when teams have multiple site collections and want to track documents across those site collections, but useful when all teams sites and subsites are in the same site collection.
For completeness I created a sub site to the Site2 Site Collection:
http://teamsites/teams/Site2/SubSite/
Then I uploaded a new file to the document library and it was given the ID "TEST-3-1"
The URL to this document is:
http://teamsites/teams/Site2/SubSite/_layouts/DocIdRedir.aspx?ID=TEST-3-1
This URL also works (lack of SubSite in URL):
http://teamsites/teams/Site2/_layouts/DocIdRedir.aspx?ID=TEST-3-1
This URL does not work (because DocumentID feature is not enabled):
http://teamsites/_layouts/DocIdRedir.aspx?ID=TEST-3-1
Enabling the "DocumentID Service" Feature on the "http://teamsites" Site collection and retrying the URL "http://teamsites/_layouts/DocIdRedir.aspx?ID=TEST-3-1" give the error message "No documents with the ID TEST-3-1 were found in this site collection."
Hope this helps