It could become a thorny issue, but if we brought together all the competent parties in the same room, I don't think it would be too difficult to come up with an agreed-upon protocol on the way to solve these differences of opinion. I'm supposing here that all such differences of opinion should always be resolved in favour of the witness. If one of the two groups has the impression that increased protection should be provided, that type of protection should be chosen and the witness should always be given the benefit of the doubt.
In reality, I don't think this would be very difficult. My knowledge is limited, because like you, to me this is a little black box within which I try to guess what's going on in this system. That said, to my knowledge, very little information is made public right now. I think that the conflicts that occasionally take place between police forces on the level of protection and so forth almost always involve a matter of cost. Ensuring protection costs a lot of money, and not everyone agrees on the need for that expenditure. If the question of cost and sufficient resources can be solved, many of these debates will cease to exist.