The capture targets are brainwashed, so their idiocy is... understandable. Not necessarily forgivable, but that's up to their respective fiancees.
As for the "heroine", she's not sane either. Not brainwashed in the same way, but she's delusional as she considers that she's the heroine of a game and thinks that everything just must turn in her favor. I suspect her family, or someone close, took advantage of her and her "prophecies" to gain power and encouraged her to indulge in her delusions instead of dissuading her.
She also was proven a liar on all accusations, and went the extra length of yelling all her plans and delusions in public. She was visibly not prepared for any unforeseen circumstances, so the (likely) mastermind who supported her was probably prepared to cut her off at the first sign of trouble. Heck, these circumstances should have been very foreseen given how she didn't manage to feed Rufus even a single cookie.
The king is a bit suspicious as he basically let his son get drugged and brainwashed, but there are several factors that might weigh in. He has enough authority that he can likely judge Miss Heroine with little evidence. Just enough to convince him would be sufficient. But he likely want to make sure he gets all the cunning people involved with her instead of just catching one crazy lady dumb enough to yell her whole plot in public.
And this exile has zero chance to be enforced. The brainwashed prince doesn't have the authority to exile two people his royal father considers as vital elements to the country. Pia being a national secret level asset might be revealed for shock value, but Rufus himself has been extremely active as acting Prime Minister. No way in hell the king will favor an impulsive decision made under influence over two extremely talented individuals. He might or might not reinstate his foolish son after rehab, but right now what little authority the prince has is basically easy to circumvent.