the video clearly shows her showing the key card to Chairman Bloom.
Key cards are not ID - of course it was a key card to the pool. That doesn’t mean she was an actual resident in the commmunity.
As I pointed out earlier the common rules are that key cards cannot be given to guests and a resident must accompany guests at all times.
The video shows her handing A key card to Mr. Bloom. What proof do you (or did Mr. Bloom) have that its hers? These things get lost, or borrowed, or improperly loaned.
You should be careful claiming as fact that which is actually opinion.