I have to come down on the side of RDP access for DBAs.

I have seen many cases where there was a problem with the server and the Windows admins claimed there was no problem. For example, a Windows admin claimed they saw nothing wrong with disk performance when I was able to show that the IO performance was only about 5% of expected throughput.

DBAs often have as much server knowledge as Windows admins because of their greater experience, and may be more motivated to actually find the problem.

IT is a team and you don't want to keep you best players on the bench when there is a problem.

I think you will find that very few DBAs a reckless enough to cause problems with the server, any more that Windows admins are reckless. DBAs tend to have a very conservative approach to these things.