Putin decides who gets responsibility for the attack. Right now he is of course putting much of the blame on Ukraine. Doesn’t matter who really did it.
The reason that theory doesn’t work is that Russia’s decisions about Ukraine are already made. There is no need to generate any stories about Ukraine involvement because the decisions are already made and in place and actions are underway and relentless. There would be no value to another story. It would change nothing so there is no reason to manufacture one.
I do question why they had travelled 100 miles+ before being picked up. That is puzzling.