Good points.
To answer your questions:
Who was the operator handing out baseball bats from inside the Capital?
— probably a fed**.
Who pushed the button to unlock the heavy doors at the Capital.
— probably a fed**.
That Sullivan fellow is a Military brat, right?
— probably.
** includes Capitol police.
(You)
— probably a fed**.
— probably a fed**.
— probably.
** includes Capitol police.
But, we just found out that the DoD NOT DoJ was running the security OPS that day.