Why didn't John Connor give a good cover story to Kyle Reese?

Question

In Terminator, Kyle Reese is arrested by the police and promptly treated as a raging psycho by telling them about time traveling Rondos robots.

He was sent by John Connor, who - as we are given to know via backstories from T1 and especially T2 - had quite a lot of (mostly successful) experience of dealing with the cops from the somewhat-wrong-side-of-the-law.

Why didn't Connor bother giving Reese - as part of his mission briefing - the idea that he might run afoul of the police, and how to best handle the situation in the least damaging way?

Answer 1

Based on the transcript he didn't have much time from when they discovered the time machine to when he was sent back.

However, Kyle must of have been briefed or had knowledge of some things. For instance he knew to run away from the police (initial scenes). He also knew that police cars were a place to potentially acquire weapons (such as his shotgun).

Additionally, how was he supposed to play it cool with the police? He was a suspect in a double homicide of Sarah Connors and he had essentially kidnapped another one. He was involved in a hit and run (with the Terminator) and a shoot out at a club. What was he supposed to say to the police to convince them to let him go? From a court perspective the insanity plea was his best bet.

He was also under emormous time pressure. He knew the Terminator could easily find them, knowing that they had been taken by the police. He basically tried to lay it out straight in the bleak hope they would help him to protect Sarah Connor.