Except that Lt Vance says that Lanza was not buzzed in. And there is that police dispatch reporting broken glass in the window next to the front door. I think they may have then broken more of it to make it easier for themselves to get in.
Yes, Lt Vance said that Lanza "wasn't let in willingly". He wouldn't say that Lanza shot the window out to get in, but he did admit that the 'swat team' members did break a few windows upon entry.
It seems logical to accept Lanza shot his way in.
But I wonder why Lt. Vance avoided saying Lanza shot out the window.