It seems the crux of establishing Jay as a flaky witness vs a complete liar totally coerced by the police, comes down to did he know the location of the car before the police or not. So I've been looking more into this.
This document implies the police were still looking for the car on the 27th. It contradicts the news report posted earlier, but while they might purposely misdirect the public I doubt they would waste the transit authorities time asking for help looking for a car they already knew the location of, I can think of no reason for that.
That same evening of the 27th (into the 28th) is when they first interview Jay,
here's the transcript. Jay says the car is on Edmondson Avenue four blocks down from where he met Adnan and he can lead them to it.
This still looks to me more like Jay knew the location of the car before the police.