JP has horses scattered all over the place, it's not possible to view the horses running in his colours as part of a single entity, still less a "well oiled machine". JP buys horses and leaves them in situ, and he doesn't jump in and start changing plans already made.
The first time he set eyes on Capt Cee Bee was in the parade ring at Cheltenham the day he won the Supreme. Who did he beat? Another JP horse, Binocular. AP didn't know which one to choose, and in the end plumped for the wrong one. There was no question of redirecting either horse elsewhere.
The O'Neill stable would be different to most of the other stables where JP has horses, because he owns Jackdaws Castle (I think) and Jonjo is virtually a private trainer for him. This, and one or two other stables (Madden?, Roche?) might be part of a closer operation, but I reckon the dozens of others who train his horses are left to do their own thing.
Ardross, I'm sure AP's opinion is taken very seriously, but if Eddie Harty wants to run Captain Cee Bee in the Champion Chase his opinion will also count. After all, he has already delivered one Cheltenham win, and the horse is clearly very high class. It's a strange notion that AP would attempt, or be allowed, to veto his participation.