It is under your premises. Congratulating them on a "Job well Done" is literally saying "You did this thing good and I approve of it." It is a criticism/critique/etc, and is being done so publicly, which is what you are stating, is a nono. As I pointed out, saying nothing also falls into a public criticism, so does saying it to some and not to others. Because the issue isnt you, its them. How they receive it is where youre placing the emphasis. How they 'might' or 'might not' take something is determining your actions, when in reality at some point you got to just throw up your hands and say things and let them sort it out.
It seems like you get the flaws of your point, but dont want to take it to the logical conclusion. Doing it in private does not guarantee anything because you cannot control how the other person feels about anything. Even if done privately and politely, it may be taken as rude and offensive and there isnt a lick of anything you can do about that. That is the nature of human interactions - sometimes, even at your politest, people take it poorly.
It seems that to you, politeness means sparing embarrassment, because offering advice, even in a tell, is criticism. So you arent sparing them that. And as I already addressed, you have no guarentees of sparing embarrassment either.
You are still screwed no matter how you cut it by your metrics. You run the risk of embarrassing them, criticizing them, etc whether its in a tell or in public. No matter how you couch your language, they can take it negatively.
The only thing you have control of is what you say and do - and for the sake everyone involved, it makes more sense to (politely) offer up advice to help correct an issue in real time than to sit back, do nothing, and wait for the duty to end or fail before saying a thing. Which at that point you still have all the same risks involved that youre trying to avoid.