Thanks, guys. I can see how my OP wording might have been confusing to the student so I went back to my outgoing messages to check the wording I used and discovered I said this:
Lisa has appointments available at either 8:30 am or 9:00 am on Wednesday. I know this is short notice, but since the semester starts next week (student had only completed her paperwork on Monday) we'd like to schedule an interview. Please call me at ### to let me know which time is best for you. If you can't make either time, please let me know if there is a better time to arrange the interview. My office hours are M-F, 8:00 am-4:30 pm
This is one of those things I would say where to me, it's obvious that there's no appointment made until they call me back, and they need to call me back by 4:30pm. But, IME, a fair number of otherwise reasonable and responsible people would not catch the deadline. Or, due to life, they would not get my message until after the deadline, and then would be in a quandary about what to do. Responding late and then showing up at the given time, even without confirmation, to me seems like the best option at that point--isn't the other option to blow off having an interview at all, and cancel one's plans to attend school there? That's pretty serious and in the student's position I would do everything I could to patch up the situation and still get my interview.
Of course, a lot of it is attitude. If I were the student I would be apologetic and understanding, and offer to come back later if it seemed that the wires had gotten crossed--after all, I'm the one who needs the school more than the school needs me. So if the student was snotty or entitled in her attitude I can see how that would rub the OP the wrong way, and would be rude in and of itself.
OK, clearly I need to think more before responding sometimes.
*After further thought, and comments after mine.*
I do believe the student bears much of the responsibility, as if this was important to her, she'd be doing whatever she could to schedule the interview ASAP and be there. I've not in the past decade met a teen-20something girl who isn't constantly looking at her phone for various reasons. The phone will make a noise alerting you to new email or text or voicemail that needs to be checked, so you don't have to be looking at it constantly. If one is waiting on something important, one stays aware of notifications from the phone.
That being said, I agree with wolfie and Lynn2000, that if I had gotten the message after the deadline, I'd probably show up as well, on the off-chance one of the times were still available. As Lynn says, however, it's all about attitude. Knowing I hadn't confirmed an appointment, I'd be hoping to be worked-in somewhere in Lisa's schedule, or come back another time.
I also find it odd that the week before school starts, Lisa would be cutting back her hours, rather than making herself _more_ available for last-minute interviews and the like. I agree with others if 8:30 and 9:00am are offered as available interview times, Lisa should have been in the office at those times. This late in the game, it may be wise to have open interview hours, where walk-ins are accepted (though they may have to wait their turn). It was nice she could get herself into the office reasonably quickly when the student did show up.