First of all, teachers don't like to have to be the bearers of bad news so it is natural that perhaps she wasn't her usual chipper self.
Try not to be so defensive; many kids bite and get bit. It *is* standard procedure to report all biting (whether the kid was the biter or got bitten) in many daycares; at ours an 'incident report' is filled out and parents are notified at pickup. Your kid probably wasn't walking around, bearing his chompers looking for his next victim. More than likely he was either trying to get a response out of another child or was expressing an emotion for which he didn't have words. While this isn't the greatest of behaviors and we don't want our children to repeat these behaviors, this is fairly NORMAL so try not to take it so personally like your kid committed a terrible act.
My kid has been bitten a few times in daycare, mostly because he did something to instigate the biting (taking a toy or a book) but sometimes just out of the blue. Do I want to know about this at pickup time? You're darn sure I do - I don't want to get home and find bite marks with no explanation. My kid also bit another child at daycare and you can bet that once I found out about it we swiftly took steps to get him to use his words and not biting.
So, yes I do think you're over-thinking this. You even say if your child got bitten, you wouldn't think much of it...so since your kid bit another kid and the teacher said "he bit the other baby...so it wasn't a big deal", then I don't know why you'd get all upset about this. Don't let your feelings get hurt because your baby bit another kid; while it isn't a desirable trait and embarrassing as a parent to hear that our children do things like this...it is NORMAL (unless of course it becomes a daily occurrence, so work NOW to nip it in the bud).