Change Private Status via Import

I thought I could do this, but I'm getting an error.

I have a user who accidentally marked a contact as private.  And the contact not only wasn't his, but someone who is out on maternatiy leave right now.    So I'm trying to figure the best way to get this contact fix.  (And yes, I'll be taking that private box off the screen for that user.)

Anyhow, I thought I could export the contact, manuipulate the CSV file, then reimport.  But when I do this, I get an error on the import that it can't find my record.   Perhaps I'm doing the import wrong, but I'm selecting "On Demand Row ID".   Then I'm matching the "Contact ID" that I exported to "Row ID".     Is this not correct?    Or does that "Private" selection still prevent me from updating it via an import?