Well, the cop made a series of mistakes:
1. The first thing I got was that the officer almost immediately treated McNair like "
one of the boys" instead of a person of interest; not the smartest move in his line of work. He (
the officer) almost felt at ease as soon as McNair told him that he stayed in a hotel just up the road and is into roofing. So at ease that he leisurely smoked the rest of his cigarette.

2. Also, when the officer first asked McNair what his name was, McNair replied, "
Robert Jones"; the officer then began wiping dog crap off the bottom of his shoe. Later on the officer again asked him his name and McNair replied, "
Jimmy Jones". Hello! Red flag here!
3. The officer didn't ask for the "jogger's" social security number either to verify his personal claims. Since he didn't have any ID on him or a local home address, seems like a reasonable request being that they're looking for an escaped convict and all.
4. The officer admitted that this "jogger" couldn't be the escapee because he would have run away by now. That's a common assumption since 99% of all crooks & fugitives choose "fleeing" as the route-of-choice to escape justice. 'Course if you have nowhere to go, deception seems a viable alternative to capture-- depending on how you look at it.
But standing in the cop's shoes, this doesn't "look" like an escaped convict either. He doesn't have on prison issued fatigues and he's carrying a water bottle with him. True, he may have had enough time to change, get a shave and swipe a canteen- but I can see some of the doubts he must have had.
I bet the guys at the precinct and McNair are still laughing at him.