Correct - stallion owners have very little control once the semen has been shipped to a buyer. The buyer may use it in the mare they declared to the SO when they ordered it (assuming it is an SO who wants to know that info), or the buyer may use it in a completely different mare (with or without permission of the SO), or the buyer may store it for future use, or split the doses to use in multiple mares, or sell the entire dose or part of it, yada-yada. Even if they violate a contract with an SO and āmisuseā the semen, there is very little recourse for the SO short of suing the MO and that is rarely worth their time and trouble.
As I mentioned upthread, registries used to try to help protect the SOs by demanding breeding certificates signed by the SO before they would issue registration papers, but in this era of shipped semen - particularly frozen and ICSI doses - it is very, very difficult to stay on top of. The registries need the money from foal registrations so they are generally not as stringent about policing registration of foals produced via frozen/ICSI. Although some registries try to do a better job of it than others, the fact that KS is able to register foals with KWPN that were produced from frozen semen that has likely changed hands more than once is basically proof that the registries arenāt going to try to help the SOs manage that aspect of their breeding businesses anymore. IOW, the registries are pretty much telling the SOs they are on their own when it comes to tracking and policing the use of any doses they sell.