I disagree with Sasha on this part: "So, I suppose, author here is creating some contrast to "правило доброго тону" (maybe something similar to the carrot-and-stick method or something related to "you can get much further with a kind word and a gun than you can with a kind word alone", or maybe they had some other thoughts)."
There is indeed a wordplay here. "Pravylo dobroho tonu" is a "good manners rule." That is a phrase we use a lot in everyday speech. "Pravylo dobroho remenia" is a "good belt rule." This we don't use a lot or even at all.
Let's take a look at the words of this song:
Справа в тому, //
Що в мене немає дому //
І за правилом доброго тону, //
Як за правилом доброго ременя, //
Я згадаю з якого я племені, //
Пригадаю з якого міста, //
Я чекаю на своє Греммі, //
В мене просто нема де сісти //
Написати свою промову: //
У мене немає дому...
As a lot of songs of Odyn v kanoe are about violent things happening to Ukraine in the past, this "good belt rule" may be a bitter irony about the "good belt rule" ruling Ukraine instead of the "good manners rule."
Another proof of this is that this song is partly about Internally Displaced Persons, one can try reading comments under the video on youtube, one will see that there are hundreds of IDPs claiming that they felt connected / were crying / can't forget their homes.
Now look at these rows again: "Пригадаю з якого міста, // ... // В мене просто нема де сісти // ... // У мене немає дому..." Let's translate it: "I'll remind myself of my hometown // I have nowhere to sit // I have no home."
Now let's think about it, is it good manners rule or good belt rule, when someone is forcing you out of your hometown? Was there a choice? That's my argument against Sasha: I think, it's not a connection between those two rules of manners and belt, it's about the juxtaposition of those two rules, of bitter awareness that our habit to live by the rule of good manners is often interrupted by the guys trying to imply the rule of good belt on us.
As for me, the allusion is not vage, it's bright, strong, and bitter. "The rule of the good belt" is connected to our past and our psychopatology and linkage to violence that lives in us cause of the postcolonial, postgenocide state of our society that we are trying to overcome.