The way I read the OP, and his reply email, was that he didn't get her message and therefore assumed that she hadn't gotten his.
In other words:
12:45. He sends a message asking to reschedule.
In the meantime, he hasnt heard back so he thinks she didn't get the message and does his best to get there close to 330.
She sends her message after he has left, so he doesn't get it.
He gets to panera late and, believing they still have plans at 330, thinks he's arrived too late and she's already left.
She returns from the pet store and has missed him.
Maybe I've misread his message. But assuming this is the case, what she wrote in her message doesn't matter since he didn't get it.
It seems to me that if we have to attribute fault in this, it's with him, since he tried to change the plans. But I don't think fault is necessary here. People's lives are very busy, it's understandable to need to make a slight tweak to plans. If you don't have phone numbers, communication is difficult. If he hadn't sent the original message, if she hadnt left, if he'd stuck around just in case - they would have found each other. Nobody did anything wrong, IMO, just an unfortunate series of events.