Respecting someone's beliefs is important on matters of opinion. Religion and politics are examples of this. I may not agree with you or any other given individual on a given subject, but as my opinions are not objective fact it behooves me to accord you the right to hold your beliefs in the hope that you'll extend me the same courtesy.
You have no reason to respect a belief that's based on factual errors. In fact, I'd go so far as to say that you have a moral obligation to rebut such beliefs and dispel them, if you're able to do so. However, it's important to respect the individual regardless; approaching it the way you did effectively shuts down dialogue, which means you get nowhere. Respectful disagreement is always more productive.
My policy is to always give a person the benefit of the doubt. I assume that the other party is an intelligent and rational individual who is simply misinformed, unless or until proven otherwise. I also try to remain open to the idea that I may in fact be wrong as well (and thus, you'll often see me using phrases such as 'correct me if I'm wrong,' or 'It's my understanding.') Of course, the latter doesn't really apply in this case; the events you've mentioned are not in any way controversial and are pretty much a straight refutation of what the other student claimed. Regardless, had you approached it in a less confrontational manner it may have opened the door to a debate on the hows and whys of these events. Without knowing the context of the class I don't know how well that would've gone, but all the same.
I don't know your school or your professor, so it's hard to say. Had it been me (ha, as if I'd sit through school long enough to become a professor), my objection would not have been to the rebuttal itself but rather the way it was fashioned.
This is my opinion. I ask you to respect it.
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I wake up in the morning more tired than before I slept
I get through cryin' and I'm sadder than before I wept
I get through thinkin' now, and the thoughts have left my head
I get through speakin' and I can't remember, not a word that I said
- Ben Harper, Show Me A Little Shame
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