A roulette is a cooperative environment, meaning the input of your fellow teammates does matter. This is like sitting in a work environment and letting a fellow colleague continue to do something that is slowing down the completion of your project and you are suggesting that "Oh, dont say anything publically, pull them aside and do it privately. Otherwise youre being rude." This makes even less sense because the actions of a fellow colleague may end up ruining hte project and it cannot wait til after wards to be addressed. Life is complicated, sometimes things have to be addressed on the spot. Now how you do that is in your control, and to what degree is as well.
And the issue that you keep stumbling over is that you keep conflating calling out, criticism, and advice as all being inherently negative if done publicly without request. Your position, in response to all this, is to not say anything at all in a public setting otherwise it is calling someone out or applying criticism/critique and is rude.
Again, quoting you: (In regards to my comment about advice vs calling out and criticism)
The issue with this stance comes down to two major issues: The intent of the speaker and the interpretation of the listener.
As I outlined earlier, by your own line of thinking, congratulating someone at the end of a run is also not allowed and rude because that tacitly implies critique of their performance. If you want to take that one step further, if you fail to say anything, you can be construed as tacitly disapproving their performance, or if you choose to congratulate one person but not another, you are giving approval to one and implied disapproval to another.
If you take a hot second to think about what is being stated, it's essentially a 'damned if you do, damned if you dont' scenario where your motives and intentions are decided by the interpretation of the other party and not you. This isnt a functional model to work by, particularly in a group co-op environment.
The other side of the issue, the interpretation of the speaker, undermines your basic logic - That it is less rude to do it privately. Offense is always taken, never given. While that little saying is a bit simple, the concept is that no matter what you do, it is ultimately going to be the receiving party that will decide if theyre offended or not. So whether you do it in front of your party through any means (criticism, critique, advice, callingout, whatever) or you do it in private through a tell, if the receiver thinks youre being rude, youve accomplished nothing. You have not done anything less rude, because the listener assumes your intent to be rude.
Quite literally "I didnt ask for your advice, so stop whispering me. It's Rude." The only thing you might be sparing, and that isnt even guarenteed, is the potential embarrassment a person in front of other people. But if embarrassment is what youre hoping to spare a person from, doing it in private doesnt solve that because at that point you are affirming that you knew the player was doing things that encouraged you to whisper them for advice. So now theyre embarrassed you noticed (or potentially so). Even if you couch the message with "Hey, did you want advice for 'x'", you get the implicit implication that you think something is up and they need help/coaching/advice.
It does not matter how you frame it, how you do it, how you go about it, by the way you suggest you encounter the very same problems - not avoid, and depending on the interpretations of the listener, your actions can come across as even ruder, possibly patronizing, because you decided to 'call them out' or 'criticize' them in private rather than giving them the dignity and fairness to assume that theyre a mature person who can handle advice and criticism fairly in front of others.
It's lose/lose by your metric.