When I click on “Close” (under a question), I get a “Why should this question be closed?” dialog box. If, in that box, I click on “off-topic because…”, I get a “Closing > Off-Topic” box. If I then click on “Other (add a comment explaining what is wrong)”, a “Comment” box appears. The text that I enter into that box is, in fact, saved to the question as a comment that anybody can see. It seems like this is a custom close reason, and it should be visible only to users with >3000 rep (those who can see and cast close votes), just as “other (needs ♦ moderator attention)” flag explanations are visible only to users with sufficient mojo to see and handle flags.
The idea behind this is that if you're giving a custom reason, then the user should be aware of why their question is being closed. This is intentional and by-design.