This is especially important because the subject matter is formless: just mimicking what the teacher appears to be doing externally would never teach what's going on, especially because most of the time you can't even see it. So there is a great emphasis on verifiable transmission, to make sure you're actually getting everything.
I agree with the above. The subject matter is formless. that is why you need a good teacher to explain what you are supposed to be doing. As to the 'ki tests' they have two purposes not one. The first as you discussed is to assess and verify transmission of these skills. The second and most important IMHO is to help the student develop them in the first instance.
The tester at all times is helping the student to find their centre, he is giving them external feedback to help them understand what they are supposed to be doing. One reason people often 'fail' a ki test is that they see it as a test, something they need to pass or fail and this encourages the state of mind that causes them to resist and fight back. Once you learn that the tester is giving you a present, giving you ki to learn with and to understand what you are supposed to be doing with that formless aspect you described, things tend to get easier.
A part of the problem I have as the teacher is that when giving these 'tests' (which are actually just me helping them find and use their centre) people often see me as being their assessor, because I'm the guy out in the front of the class doing the teaching. I've found that the people who seem to have figured out that I'm not trying to pass or fail them when I do this stuff are the ones who see me less as 'sensei' and more as 'Mike'.