As funny as I find those jokes, there's a major problem with them: many of the people harping on about the Trump-Putin lovefest also harp on about how Trump's an unstable lunatic.
So what do you think someone that unstable might do to show that he is not, in fact, Putin's bitch?
"Launch the nukes! Send in the troops! This war will be tremendous! We'll be winning with this war!"
And then, oh fuck, it's WWIII.