They are speaking from the perspective of a manager, so HR isn't leaking identities to them.
Although based on what they are saying, I don't think it would be hard to de-anonymize this info - exit interview feedback looks different than general feedback, and if it's in any way specific (and if it's unspecific it's not super useful) it's almost always easy to identify who it's from.
Of course, they don't get an embossed label with the name(s) of the one provided feedback. However, depending how high are they on the ladder - even directly asking may yield results.
What struck me was the belief 'all feedback', e.g. no exceptions, no redacting that may reveal details, no language replacement.
The other issue is mixing with w/ regular feedback - aside personal integrity what's the reason for anyone to be honest on an exit interview.
Although based on what they are saying, I don't think it would be hard to de-anonymize this info - exit interview feedback looks different than general feedback, and if it's in any way specific (and if it's unspecific it's not super useful) it's almost always easy to identify who it's from.