From what you describe in the original post, yes, the DBA's can probably do everything described without RDP access. You can view the event log, file sizes, etc. etc. without RDP access. That is going to require some work from the server team, however.

It really sounds like some education is required. The server team needs to better understand exactly what the DBA's do for a living, and the DBA's need to understand the requirements of security, auditing, etc. etc.

Once this education occurs, an assessment of the practices on both sides regarding compliance, documentation, and so forth should occur. Bring in someone from a different department as a referee!

We have admin privileges on all of the database servers, and additionally have been granted the rights on the physical hosts for the virtualized boxes.

The DBA's rarely use RDP to get into a server. But, we work together as a team and follow the rules set forth by all parties.