Yes, you are seeing that correctly.
Let's do an experiment.
Grab psexec from Sysinternals. Transfer it to to your domain controller.
psexec -s -i cmd.exe on your domain controller.
Now in your new command prompt, type
whoami /groups. You will see that you are now the SYSTEM account on your domain controller (aka DC01$) and that you do indeed belong to the Builtin\Administrators group.
Those builtin groups are shared among domain controllers. So here's something neat:
start \\DC02\c$ from your command prompt. It should launch Windows Explorer on your other domain controller because you (DC01$) are also an administrator of that DC as well!
Domain controllers do not have a local SAM in the same way that regular Windows machines do. (Well they do but it is only used in restore mode.) They all share the AD Builtin groups, and since a Windows system needs to be an administrator of itself in order to function, just like any SYSTEM account on any other Windows machine, that gives us the interesting side-effect that all domain controllers end up being administrators of one another.
Edit: Cleaning up for posterity.