I don't believe what he said about YZ panicking and therefore him letting her out of the car. I think he made the panicking part up as a plausible explanation of why he let her out at a point other than her destination. A lie to go with the lie.
I think she knew him (if only by sight) from campus, she might have known that he was advising students, so she trusted him. There's no hesitation or awkward body language before she entered his car. He then probably proceeded to tell her some yarn, possibly that he's subletting his apartment for cheap, and she was willing to have a look at it. I think she went into his apartment alive and well, therefore nobody heard or saw anything out of the ordinary, and it was only then that he showed his true motive.