In the single most unprofessional interview I've ever suffered, the interviewer double-booked the time slot. The interviewer--dressed in a shabby sweater--walked over with a scowl. We had corresponded and set up this date and time. He saw two people waiting, and instead of greeting us, he hollers, "who arrived first?" The other person indicated they were first, and he said, "Okay, I'm [name]." And had this person follow him. No explanation, no greeting.
Assuming a break-down in communication (but put off by this guy's managerial incompetence and manner), I emailed a polite refusal to the invitation to meet. He emailed back that they schedule in blocks and if I can't wait, well, they don't want me either. I've declined a lot of positions, but never has anyone been so petty and defensive about it. I'd stay far away, if possible.