They have no reason to do that. They're allowed to put out a deceptive narrative that this is all happening because Trump changed something. And that is superficially true. What they leave out (or minimize) is that what changed is that Trump has decided to start enforcing a criminal statute that has been on the books for decades. Why leave that out? Because it implies the obvious. Obama (and Bush and Clinton and Bush 41 and Reagan) basically were derelict in their duty to enforce the law that Congress enacted. And of course, it becomes much tougher to bash Trump in the equation. How do you blame a president for enforcing the law? That's his whole friggin job.
They would rather state it another way even if they acknowledged the law: Obama cares. They don't care about the law. They care about appearances and I think we know they supported any executive order put in place by Obama regardless if it was clarification of policy under the law or changing the law itself.
I saw a video recently (an interview of Obama). In it, the interviewer started out by saying Obama was deporting close to 1,000 people per day. Obama did not object to this fact or stipulation. He knew it was true. Later Obama discussed the Dreamers's and it was for them that he made the policy changes as we know, citing limited resources to comply fully with the law. There was no mention of separating families or what they did with children at the point of apprehension wherever it may be. So it IMPLIED that he followed the law other than the Dreamer deferred action order. But did he? Because following the law in theory is ZERO TOLERANCE.