Two choices: either Hillary Clinton told Democrats what she thought they wanted to hear,

with little intention of actually doing anything, or she's playing the Bill Clinton "go over every word to try to figure out what she actually means" game.
I'm just going to focus on what she said when Chris Wallace confronted her with something she said last year, "The Supreme Court is wrong on the Second Amendment."

WALLACE:  Now, in the 2008 Heller case, the court said there's a constitutional individual right to bear arms.  What's wrong with that? 

She responded and — forgive me — I've got to parse this pretty closely:

CLINTON:  Well, I think what the court said about there being an individual right is in line with constitutional thinking.  

Is the "constitutional thinking" she's referring to there wrong, in her view? She doesn't say. She repeats the majority's interpretation and essentially says that was an interpretation that existed out there in the legal literature. 
And on.  And on.

I’m not looking to take people's guns away...

That's just a policy — a policy the government could enact even if there were no individual right to bear arms. So we're very far from the original topic now.

... but I am looking for more support for the reasonable efforts that need to be undertaken to keep guns out of the wrong hands.  

So you are for the policy of taking some people's guns away. The wrong people. (And speaking of wrong, was the Supreme Court wrong on the Second Amendment, in your current opinion? I still don't know.)Even if it stopped there, who all does she consider the 'wrong hands'?  That phrase give you any comfort?  It doesn't me.