My sister got into a slight fender bender this morning and the other party didn't want to call the police or exchange insurance information because she said there was no damage. She later called saying she took her car to have it looked at and there was a dent in the bumper. Since she waited until after the fact, is my sister obligated to exchange insurance information?

How much was the damage and is she planning to pay for it out of pocket ?

I don't know that much. I live out of state. But my sister claims that it didn't even knock dirt off the bumper and tried to return the call but there was no answer.

If this person is asking for money then she needs to exchange info.

She does not have to give her insurance info, she can merely write them a check or wait for them to sue her in court.
But the best thing to do is give the insurance info and report to your agent about it, and that there was no damage at the scene.

Also remember if one side does not want to call police
Normally

1. they don't have a drivers license or not valid
2. they don't have insurance
3. they are not legal citizens
4. they are wanted for some other crime.