That's not necessarily true. If the reason that the person is turned down is that they are massively over-reaching their experience then there is a good chance that they will experience the same rejection elsewhere.
If they want to take that on board, it's up to them and it might well be helpful moving forwards.
I will personally give people feedback if its tangible and reasonably objective but if someone just feels wrong, I think it is easier to say they were not a good fit and leave it at that.
A company didn't think you are a good fit. That's it.
The criteria they used to evaluate that is totally different than the criteria other companies will use.
What is the point of providing feedback for a data point that does not correlate with other interviews?