He has no obligation to show a key to a stranger.
SHe opened the door, and he tried to come in. If she lets him in, and he robs someone, she is an accessory to the crime.
She had every right to ask him to show that he had the key to that door, assuming her story is true — and nothing in the video or what the guy said suggests otherwise (He says something about having been “buzzed in”, which would also indicate that he had no key. Not sure why he would have gotten “buzzed in” if she had the door propped open already, so I’m not completely buying either story at this point).
According to her, the condo had REQUESTED that people be responsible for this security.
She was under no obligation to let him in and shouldn’t have.
And she has no obligation to allow a stranger to enter on his word that he lives there.