How might you reasonably challenge the way the professor reached her conclusion?

One way to confront the professor would be to ask her to explain once more how she got the conclusion that she did. This way could cause her to catch a mistake if she made. If there is no mistake and there is simply a disagreement, then a student could also continue to ask questions as the teacher is explaining the solution. What if type questions could also be asked. Asking questions is a good way of not being disrespectful to the teacher.