People seem to be falling into two main camps: "she has a right to charge you" and "it's unkind to charge for circumstances beyond your control."

Both are true. Of course she reserves the right to charge you, but it seems like a total lack of compassion to do so. And the whole "but being rigid and consistent constitutes good boundaries" argument? No. I don't think so. If you rely so heavily on rigid and consistent rules cause you think that showing a bit of humanness is violating some big boundary, you probably aren't therapist material.

Talk to your T about it. If it was her oversight or you were charged by office staff, it'll be good to clear it up. If she really is that rigid and your having been sick makes no difference to her, well, that's a sad and painful thing to learn (or would be for me) but is still useful information going forward.