That idiom is talking about if you overly help that someone, they Become dependent, and when you stop helping them, they hate you.
First of all, that can also applied to Russia and China, in fact, I personally know quite a few Russian who started to hate the Chinese for dangling them to be punched by NATO while they think China didn't help enough as "Blood Brother"
Secondly, this does not applies in this case, because we aren't talking about a person who may be down on his luck or whatever, we are talking about a total annihilation scenario. Again, whether or not the American or West help them, that's not going to change how they hated the Russian. Because this is a fact that they invaded Ukraine, and start killing their neighbor. This is like Iraq, or when Japan invaded China, how much do you think the Sunni and Shia in Iraq hated each other, but when we come in, we give them a common enemy, whether or not they hated each other, they hate us more, same thing happened to Japan when Communist and Nationalist in China was fighting each other, and then the Japanese comes in and started killing your neighbor whether or not they are communist or nationalist, that changed pretty quick.
You ask me whether or not I think they won't change? No, people change, but will they go back to Russia when it was the Russian dressed in green come into Ukraine and murder their neighbor and rape their children? I can tell you this, they don't really like American over in Ukraine, in fact, they see us as arrogant, and now indecisive, but does that mean they will like the Russian more? Well, I will let you find that out.