I used to administer instruments (tests) like that.
In most cases it was a successful and enjoyable activity, and there wasn't this confidentiality issue because we structured around that.
However I also made it clear that the whole point was understanding how to embrace differences. So sharing one's personal reported result, while optional, was done a lot.
But in a couple of cases, people like the boss took the activity way too seriously, no matter what caveats or warnings they received. So either the (non)-sharer or the requester raised the stakes for themselves without realizing what they were doing, and I had to have a talk with them.
It's not really a good idea to seriously rely on results from a test with some known, significant, and published (by the authors) accuracy, validity, and test-retest error. This is why the "reported result" is generally considered inferior on its own. It's also known to repeat back to you what you tell it, but in different words / models.
So, since the boss may decide to raise the stakes like that and make things awkward, etc--these days along with a bunch of other colleagues in the field I use a format that's more like a flexible, open-ended sorting exercise. It's less about who you are, and more about ways you might tend to think about things, for example.
This works around the issues above, and naturally accommodates other conclusions, like yep, some people will rate themselves differently here at work than they would at home in private, for example.
But also: We can train people to recognize the processes that they use to communicate and to take in information. Thus it doesn't matter so much what they think they "are", or what someone else thinks. The process speaks for itself. It's no longer an identity issue so much.
It's an interesting field in which there have been a lot of changes since the personality tests of the 1960s...