The scissors in the hospital belong to the hospital, so I think it should not be discussed based on majority use. However, in a hospital this is designated for permitted use (because of illness), so one should consider whether it is muktzeh at all.

Still, one has to consider the case of a utensil whose primary use is for a prohibited activity, whose status is usually more lenient than ordinary muktzeh. But regarding an item belonging to a non-Jew, there is reason to be stringent, because the function of the utensil is prohibited for me, and so it is muktzeh.
Bottom line, I still need to look into this further.

So, any progress?

A. All the sources the Rabbi brought about there being no law of muktzeh for a non-Jew’s property—was it ruled in general that there is categorically no prohibition of non-Jewish muktzeh, or did they permit it only for leavened food?
(And another small question that’s bothering me, which might give a bit of a counter to those who slander the Rabbi on his site: did the Rabbi bring these sources from personal memory, or did the Rabbi get help?)
B. Seemingly, from pure logic I would say that Jewish ownership is a condition for the prohibition of muktzeh. Let a ownerless stone come and prove otherwise: there is no Jewish ownership, and yet it is still forbidden to move. What’s the reasoning that they did not decree this regarding a non-Jew’s property?

I haven’t dealt with this in the meantime. Logically it seems to me like my later position above (that for a utensil whose primary use is for a prohibited activity one should be stringent in such a case, because at the end of the day its primary use is for prohibited activity). Still, this depends on the reasons for the decree concerning utensils, and whether it is part of the law of muktzeh. Simply speaking, it is not (it was decreed separately in the baraita from the days of Nehemiah son of Hacaliah), and its reason is apparently not that it was mentally set aside, and therefore the owner’s intent is not important here. But to write an orderly and final responsum on this will require me time.
A. I generally remembered the primary sources, but of course I searched and found them (obviously Yechaveh Da’at was not in my memory). I don’t see why that matters regarding the detractors. I don’t think remembering sources says anything about a person.
B. Ownership is a limiting condition, not a triggering one. There is muktzeh in ownerless property, but there is no muktzeh when it is not muktzeh for its owner. When there is no owner, the thing can be muktzeh, but when there is an owner, that can prevent it.

B. I still don’t understand why this law is so twisted and convoluted. Why did the Sages decide on such a definition, that if it is not muktzeh for the owner then it is not muktzeh for anyone. Also, that doesn’t seem to me to be the correct law. If a dangerously ill person needs to eat leavened food on Passover, then is his leavened food not muktzeh? Are there sources for that too?
P.S. Knowledge of sources doesn’t matter to the Rabbi? Just analytical ability? Or general knowledge too?

B. The twists are not necessarily the result of an initial decision. Sometimes this is a development of the law, which at its origin was simple. Beyond that, I think making it depend on the owner is actually quite a simple solution. It is not reasonable that the same object should be muktzeh for one person and not muktzeh for another (like the case of muktzeh for the poor and the rich, in the dispute between Beit Shammai and Beit Hillel).
In the case of a sick person, one has to consider whether it is not muktzeh at all, or whether it is muktzeh but overridden.