How to limit dynamic DNS updates
Windows DNS entries have ACLs. Check and/or set them.
Generally speaking, dynamically updated hostnames/A records allow anyone to update them, but static ones do not, but either way, this behavior is configurable.
When creating a new A record/hostname entry, you have the option to either allow any authenticated user to modify the record or not:
And it sounds like "not" is what you'd prefer. Lucky for you, that's the default.
In fact, the default settings work pretty well, in that they won't allow just anyone to poison the DNS records, or take over a domain controller's A record in the DNS table by simply renaming their machine and performing a dynamic DNS update. So unless your DNS environment is has been explicitly configured in a particularly poor and very specific way, you and your boss don't have anything to worry about.
But don't take my word for it... check the ACLs yourself, and try to hijack a domain controller's (or whatever else's) DNS records with an unauthenticated client.