UU Ministers have a covenant with each other, as do ministers of many other denominations, to honor the relationships that others have with them and with their churches. So if someone calls me to say that they belong to the such and such church and can I do their wedding (actually, this most often happens with memorial services, in my experience), I tell them I'll think about it and I call the minister of that church. The reason for the request is often some past hurt or strain between the deceased or the deceased's family and the minister. Often the minister is relieved not to have to do that memorial service. However a memorial service is not really a private affair, and most ministers consider a memorial service of a member a ministry, not only to the grieving family, but to their grieving church. This creates a situation in whcih the best solution, in my experience, is for the two ministers to work together on the memoiral service, with the "host" minister welcoming the congregation and doing the "grief work" part of the service, and the "guest" minister doing eulogy and other personal parts of the service.
All of these arrangements are a part of ministerial protocol and covenants with fellow ministers.
The new issue on the ministerial block is the increasing number of free lance "ministers" around, who usually have little training, have had no vetting or substantive certification, and are accountable to no one. They mostly don't know anything about these protocols. My limited experiences with two such persons, both friends of deceased church members with whom I agreed to share a service, were quite negative, so I don't agree to that without careful planning any more.