This is CRM 2011 Rollup 6
For any opportunity owned by this, our only team, we get the following message

This is the ID of the team itself, which is active, along with the members. The members have proper security permissions. I tried changing the owner of the team and the queue its associate with. I tried changing the email settings as well. I found one post
that suggested turning off the EMail entity setting "Automatically move records to the owner's default queue when a record is created or assigned". This did not work either.