RSBM. if she and her brother share the car, I could see it being as simple as him forgetting that she needed it that day, realizing it later and figuring that she probably grabbed a ride from someone else otherwise he would have heard from her but still calling to double-check. If I remember correctly, he tried calling but she did not answer.
regarding what she was wearing. I can see there being some confusion about the red shirt because she could have tossed it in a bag, left it at work, it could be at her house but parents missed it, etc.
it should be a little easier to figure out if she returned from the jog or not. If she did, her running clothes should be in a hamper, in a pile on the floor somewhere or wherever she put her dirty clothes when she stayed at her boyfriend's house. It's not like it is her own house where she is likely to have a lot more close to sort through, if that makes sense.
The lack of information on some of the little details (did she return from the run??) makes me think that the police know a heck of a lot more than what they are letting on.