Hi,
the NTFS permissions are the ones taking place, hence the default and best practice is to have the local administrators group set on all folder - and not a domain based group. There's a few ways to workaround this.
1) use the backup operator functionality to take files out with tools that know tu utilize it (such robocopy).
2) user-mapping, from your existing user to pretend to be another.
3) take ownership on the files, and add the required security group (painful, there's some scripts that can help - but they far from perfect).