Interesting take on it. I attribute this more to their incompetence and plain 'ol stupidity. I imagine people who can think better in general don't aspire to be school administrators. Some teacher perhaps love teaching kids and are dedicated, administration and bureaucracy attracts a special breed of people... and let's just say that these are not usually the brightest either. But what they have learned and do well is protect themselves. The constant threat or funding withdrawal from the govt, the threat of law suits, the threat of reputation if say a student goes "mental".
They have nightmares of being on the stand in court and asked questions like "are you sure you did everything you could to prevent the disaster?"...At least this is probably how testing and psych screening company sold them the packet.
Now their stupidity is also a blessing. If just someone could manipulate them into being afraid of your scenario. Being sued for collecting too much private info about its students. What if they get hacked or someone breaks into the office and steals all those answer sheets with all kinds of strange confessions? Law suits from parents is supposedly this dark deep evil always lurking in their minds. Just need to re-frame the problem so that they see collecting data = increasing risks of getting sued and voila, temporary win.
As a side note, someone on Reddit mentioned taking a similar test (but supposedly anonymous, I say "supposedly" as teacher often can tell the students by handwriting). and putting the most outrageous answers they could in the boxes, mostly for fun. I realized I would have probably have done back then the same thing, just to mess up their statistics. What if didn't end up being anonymous, it leaks and now it is attached to my name for life. Good luck explaining every employer who runs background checks.