"Umbridge was exposed" is a bit of an overstatement. What happened was that she boasted about it:
“What Cornelius doesn’t know won’t hurt him,” said Umbridge, who was
now panting slightly as she pointed her wand at different parts of
Harry’s body in turn, apparently trying to decide what would hurt the
most. “He never knew I ordered dementors after Potter last summer,
but he was delighted to be given the chance to expel him, all the
The only people present at this event were:
- Millicent Bulstrode
- A large Slytherin girl
It is highly unlikely that any of the Slytherins would have reported Umbridge's crime, nor is it likely that Harry or his friends told Scrimgeour. Indeed, when Harry finally meets Scrimgeour for the first time in Half-Blood Prince, Scrimgeour mentions Umbridge and Harry is shocked that she is still at the ministry. Even so he does not mention that Umbridge sent the Dementors, even though he does show Scrimgeour the scars on his hand from Umbridge's quill:
Dolores Umbridge has told me that you cherish an ambition to become
an Auror. Well, that could be arranged very easily. ...”
Harry felt anger bubbling in the pit of his stomach: So Dolores
Umbridge was still at the Ministry, was she?
“No, it was honest,” said Harry. “One of the only honest things
you’ve said to me. You don’t care whether I live or die, but you do
care that I help you convince everyone you’re winning the war against
Voldemort. I haven’t forgotten, Minister. ...”
He raised his right fist. There, shining white on the back of his
cold hand, were the scars which Dolores Umbridge had forced him to
carve into his own flesh: I must not tell lies.
“I don’t remember you rushing to my defense when I was trying to tell
everyone Voldemort was back. The Ministry wasn’t so keen to be pals
Thus, Scrimgeour does not seem to have known about Umbridge's crime, despite her admitting to it.