Those controlling the Oracle must prevent everyone from using other oracles or programming one themselves. If someone is capable of such total control, why would they need any service from an oracle anymore? They can indoctrinate whatever they want.

The bigger problem can arise if everyone (even 'they' in power) will be beguiled by the AI to point that any predictions issued by the AI will turn into self-fullfilling prophecies. Vicious circle.

There is a great sci-fi short story by Greg Egan "The Hundred Light-Year Diary". There is a sort of a time machine that allows people to telegraph news from the future to the past. Obviously everyone tends to blindly believe any information they get from their future self...