> Does the LDAP group submit a Grievance to your org?
If you went in and made unauthorized changes, for sure.
> Do they demand to be paid wages lost from your usurpation of their role?
That depends. If we're talking about, say, government contracting, and the LDAP team is paid on a per-request basis, and you circumvent this, yes, they would rightfully demand to be paid what they're entitled to in the contract. Of course, in this case, it's probably two separate employers in one larger organization, but it does happen.
In the case of unions, the union has a contract to do certain things in return for certain compensation. A condition for doing it at a certain price might be that the contract is exclusive. Plenty of examples of this type of pricing in the business world.
So, not really a unique union problem.