I don’t know...I watched this clip 3 times and I didn’t take it that way. I took it to mean we all play a part in our government. But I don’t think it’s the ONLY thing we all belong to.
The mom-in-chief would be pleased with how you "take" it.
We don't "play a part" in government, except that we consent to be governed. Of course we get opportunities to choose by whom we are governed... at least for now.
The words have meaning, ignore the modifiers, just read the basic declaration: Government is the thing we belong to.
Do you still take it otherwise?
Of course the titular head of the Dims could have had the words changed to "We are the government and you all belong to us."
But then that might have a greater impact on his "last" (as he whispered to Medvedev) election.
The Dims need to be made to eat their words, all of them.