ASA :
Rule 1 - Charged Conference
5.7[B]

Also, ASA RS 9-C. Since the TIME OUT was called by the umpire for a discussion with the player/coach, it would be pretty OOO to charge a conference here, IMO. Once the discussion with the official is over, and the umpire is ready to resume, if the DC wants to continue discussing things with his player, THEN maybe a charged conference, but I'd still let the coach know that if he continues, I'll have to charge a conference. IOW, if this whole thing ends in a charged conference, it will be the coach who chooses to make it such, not me.

I'm not disagreeing. I visualize the scenario as:
BU: IP
F1: What did I do?
BU tells F1, then returns to play.
DC: Blue, what did she do?
BU tells DC.
DC: Can I talk to my F1 about this?
BU: Sure coach, but it'll cost you a conference.

At that point, I've already informed F1 and DC about the infraction. If DC wants to talk to F1, I'm charging a conference. I don't see how RS 9C gets me out of not charging it in this situation.

I will answer whoever asks (coach or player only) and then will accompany the coach to the circle if he/she goes, telling him/her that I'm avoiding a charged conference, but to talk only about the IP.

But there's no basis whatsoever for letting the coach talk to the pitcher about the illegal pitch without a charged conference.
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Is there a basis for the player talking to the umpire?

Is there a basis for the coach talking to the umpire?

Is there a basis for the player AND the coach talking to the umpire?

Don't OOO this. You're not going to have a serious outbreak of intentional IPs in order to get a free conference.

The first several things are all normal parts of the game. A coach going out to visit with a player to give advice (be it on how to pitch legally or effectively) is a conference.
Suppose a runner was about to be out on a look back rule violation and the pitcher messes it up by faking a play. Coach comes out arguing for the out. You point out that the pitcher faked a play. Coach now goes to tell the pitcher not to fake plays when the runners are dancing around the bases. Charged conference?
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You've not just charged an infraction against the pitcher. This whole thing started with the caveat that handling this varies with the level of play. If we are talking about a level of play where both the coach and the pitcher need my help in understanding what I called, I'm not charging a conference if they happen to speak directly to each other instead of using me as a go-between.

Once my part is done, if they do not end it too, I'd inform them we are ready to play ball, unless the coach wants a charged conference. Then, it is his choice - conference or no.

I seriously don't see why this is such a big deal. As I said, there will not be an outbreak of intentional IPs being thrown in order to get a free conference.

Read Scott's response again, it is the correct answer.

You are correct as far as I am concerned. However, if you tell a coach and then accompany him to the circle as he tells the player, this would still fall under the domain of an official's time out. Now, if you don't go out there with him, and have no idea what instruction he may be giving apart from the IP, then you would probably have to charge him a conference. That is where preventative umpiring, i.e. walking to the circle with the coach, comes in handy!