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"Foley's Lucky he didn't get tazed or shot"
That line was very disturbing considering the fact that he was already identified as a police officer. Are you by any chance white and a Conservative?

He wouldn't have gotten tazed in 1984. The first production Tasers didn't become available to law enforcement until the mid - late '90s.

I doubt it. To my knowledge you can insult people, you just can't threaten them. Swearing at someone does not give them a license to hit you.
Did Axel shove the guy first? I seem to remember that, and if Taggert had only shoved him back I could see saying he was defending himself. But when you slug someone back you are doing something a whole lot worse than shoving someone lightly. The police officers were watching and saw Taggert hit Foley, they would have testified that he could not possibly have feared for his safety enough to retaliate. It might be reasonable to assume that the cops would lie to protect Taggert, but in the movie they seemed to want to do things by the book.
So I see it as reasonable to for the cops to offer Foley the right to press charges. If you defend yourself you have to prove that you were actually in danger, and Taggert was clearly not in danger. If Axel had thrown the first punch that would have been different, but pushing someone lightly does not justify a punch in response.
I might be remembering the scene incorrectly, maybe Foley was more threatening, but from what I recall I think the option of an assault charge was reasonable.

Could Foley have been charged for provocative behaviour, since Taggart was provoked into striking him?

coffee grounds, casing the strip club in a long trench coat in June, etx.
Bogomil knows about coffee grounds, probably because he's older and has some street experience his subordinates don't. Likely he was around before the Beverly Hills PD lost its touch?
I mean, really, how many times will you look under Jabba's manboobs?

"Doing police work that way, strictly by the book
" is what I meant to say.

Try this - become a black man a la the guy who wrote the book Black Like Me, push a white cop the way Axel did to Taggart, and let me know if the cop agrees with you that you did not strike him.
After you get out of the hospital and are able to eat solid foods again.
The point of the scene was to show that Todd's "strictly by the book" position was the beginning of his own personal story arch in learning that doing police work doesn't always get to the truth.
The beginning of BHC 2 affirms this when he squares off against the new chief, defending his men for "going with their gut hunch."
You do not put your hand on a cop in a threatening way and expect to live to tell about it. If you can, please tell us what country you live in 'cause it sure ain't the United States of America.

Well, not to nitpick the point, but Foley didn't hit Taggert at all. Yes, as you point out, he did "[touch]Taggart's person in an antagonistic manner," but really? That's considered any kind of real "assault?" In fact, Taggart only hit him after Foley threw the F bomb at him and that was it. He was more pissed off that Foley had cursed at him than that he had touched him, let alone hit him in any way. He flew off the handle in my opinion. Sort of uncalled for. As Foley said himself, he was really just looking to square off.

In a way, you're absolutely rightbut that's precisely the point they were trying to make.
What Bogamil saw was not the whole story. We the audience saw that Foley started it and touched Taggart's person in an antagonistic manner. Foley's lucky he didn't get tazed or shot.
But "going strictly by the book" without the whole story is the difference between justice and truth.
Foley came into their lives to show them that good police work sometimes demands going beyond the book.
Had Foley gone by the book, he'd have never left Detroit and a murder would have gone unsolved.
Back in Detroit, Foley told his boss Inspector Todd what the real issue was - his blatant disregard for procedure. That's a major theme in this movie, revisited in BH when Axel says "I know how to get around search warrants" and Bogamil says "we don't get around search warrants in Beverly Hills."
In fact, the entire screenplay contrasting the dingy, dank, gritty noisy Detroit police station against the light, bright glassy corporate offices of the Beverly Hills station is about how the BH operations are a superficial facade of order that lacks real world cop knowledge - coffee grounds, casing the strip club in a long trench coat in June, etx.

Acting the parrot.

Bogomil had this funny way of repeating what people say.
Rosewood: He sent us a late supper.
Bogomil: A late supper? And what did you have, Rosewood?
Rosewood: A shrimpsaladsandwich, sir.
Bogomil: A shrimp salad sandwich.
I'm trying real hard to be the shepherd.

Here in Beverly Hills, we go strictly by the book. Now, one last timewhat are you doing in
Bogomil: in Beverly Hills?
Foley: I'm on vacation
Bogomil (joining in): on vacation. Vacation.

Here in Beverly Hills, we go strictly by the book. Now, one last timewhat are you doing in
I'm trying real hard to be the shepherd.