Having sat on many panels I'll suggest there might be reasons why someone might seem rude. After a great curry the night before I once had to interview holding back what we call "Gandhi's revenge" around here. The scowl on my face probably terrified the poor kid, and then I made a dash for the toilet.

Practice interacting and being in a professional conversant situation without reading too deeply into what you think is going on for the other person. Accept the situation on face value with the best and worst interpretations in mind, but not in effect. That's good for negotiating too. If you feel on the defensive because of an implied power relation, or misunderstanding, hold that thought, wait and see, it could get interesting.

Since you allocated the time anyway, make the best of a recon opportunity. If the interviewer is being rude, the fact that you are unruffled makes you the bigger person. Smile politely and you may unbalance them. Save any grand decision for the end.