Actually that is not true.
Some police may have (there is no evidence of any actually invited in, although we do see a few standing aside as the mob stormed past), but some had also been beaten down by the rioters.
If they believed that the police were inviting them into the Capitol to smash windows and try to enter the Senate Lobby that the police barricaded as they continued to smash windows, even after the officer who shot the woman yelled for them to get back (when the guy with the blue hat acted as if he was going to enter) or he would shoot.....well ...I hate to say it but the world isn't much worse for the loss.
We have to remember a few facts:
1. The "protestors" were not protestors. They entered the US Capitol armed with various weapons (to include guns, proper spray, stun guns, baseball bats....and an ax

).
2. How did the police usher the rioters into the US Capitol? They didn't.
Looks like some remained where they were inside the Capitol. BUT how did the rioters actually get in?
They attacked and injured over 120 police officers outside the Capitol.
They stepped through windows they had broken out.
Some, after making it through the barricade, did walk right in.
But even here we saw many police officers struggling to try and get them back out.
And I am not sure that believing a police officer is willing for you to do something illegal is enough to negate the crime itself (but I'm not a lawyer....that just seems strange).
That said we are talking about two VERY DIFFERENT things. You are talking about an area open to the public. She was entering an area closed to the public, and through barricaded doors where police with guns drawn were telling the mob to stop.
BUT we were talking about a woman shot for trying to climb in a window, through a window the mob busted out in the barricaded doors as the mob was continuing to break the other window.
You think they were inviting her in???