If you feel praising in public is the only way (i.e. criticism should always take place privately), you likely were given too many participation trophies as a child

I like running, poker and oysters | Founder, Social Forensics (SocialForensics.com) | Berkeley & UPenn | Learning to listen

I see what you did there..publicly criticizing those who suggest private criticism. 

I think private criticism can be more productive, especially if one hopes to better understand and help. 

That can be done publicly, but could escalate into something unproductive if the conversation isn't thoughtfully managed.