I think it's important that I present a good image to others, which means I'm cognizant of the impression I make with others all the time. Certainly there are times I may do something that isn't professional or may offend others. However I try to keep in mind that the impressions I make are potentially those that might effect my career.
I ran across this picture. The original tweet has been removed, but I've seen it in quite a few places, so I'm guessing it's real.
Now, even if it's not, this has probably happened. In fact, I bet it's happened to quite a few people in many industries. I've run late for interviews, as the interviewer, and I wouldn't be surprised if this happened to me some day.
How should you handle this? Well, as the interviewer I guess that depends on how you feel. For me, I'd think this is the type of person that likely would take shortcuts, or make decisions without regards for others' feelings. If you felt you needed to take a parking space because you're late, at least apologize. Don't curse at someone that's upset. I'd be tempted to tell the person that they are a big disadvantage in this interview as they've shown poor judgment and behavior with others.
As the interviewee? Apologize profusely. I hope you have a reason, but you should be contrite. If you aren't, perhaps you should work on that.
We all need private spaces, places where we can unwind and vent about issues. However, if you're anywhere near a business situation, I'd suggest that you consider the person you have a conflict with just might be the person you want to do business with in the future. Adjust your behavior appropriately with that in mind.