If something cannot be tested

So now and then I hear some sounds from testers or business when I ask them to test something that they are not able to test that something.

Somehow this sounds very strange to me. I believe that everything which can be build, can also be tested. If the business were able to find an error and the developer is able to solve that error then we should be able to test the solution. So who is right and who is wrong?

I believe in my testers. My testers are not unwilling to test. They are just not able to perform the tests. And I just want to know why.

Some reasons they gave are:
1. The test system doesn't contain that situation and I'm not able to recreate that situation;
2. I don't have sufficient rights to create useful data for the test;
3. The solution is too technical and therefore it is hard to understand the problem;
4. We don't have that problem anymore;
5. I don't have time to test and this is a minor issue;
6. I know that the solution is not what I need and therefore I'm not spending any time for testing on it;
7. This problem is not my problem; I'm not able to help.
8. Who are you?

I also believe that I should convince them to test, support them to test and during testing, facilitate them to test and make the business accept the risk when they are not able to test.

If they are not able to create the data, I should see if others are able. Mainly it is because of restrictions in the system. If giving them authorizations to the system to provide useful data without messing up existing data, then this should be the solution.
If they don't have the necessary technical knowledge needed to test this, I should help them with a person who has that knowledge and teach them or help them during the test.
If they know that the given solution is not what they need, I can bring them in contact with the developer and I also have to identify how this misfit occurred.
If they don't have the time, or it is not that important anymore I should search for other ways. A solution migh be embedding the test in another test case.
If they don't know me, I might have the wrong person and should look for another tester.

Even after all kinds of actions the tester might not be able to check whether the problem is solved. Does this mean that they should not test? NO! They should at least check if the functionality which is connected to the solution is still working. Should I close the ticket after those tests? NO, not immediately, first I have the business to accept the risk that the problem might not be solved and convince them that at least the proposed solution will not harm other processes.