The weirdest interview I ever had was shortly after I got laid off from Isilon. One-fifth of Isilon had been laid off in one brutal morning, and I was among them. The economy was deep into the recession, and like everyone else who had been laid off recently I had put out my resume and my shingle, then settled into my basement to teach myself everything I hadn't learned in the previous eight years.
A large hardware-based American computer company whose name I won't repeat, but which was once headed by a former US presidential contender infamous for an ad featuring demon sheep, reached out through its recruitment efforts and asked if I would come in for an interview. They said my skills were a perfect fit for a new product they had in mind.
The interview was way the hell out in Bellevue, hours and miles from my house, and utterly inconvenient for me. When I got there, I learned that their "new product" was basically a direct competitor for Isilon's; they were trying to get into the mass storage market, and were having a hard time of it.
I was scheduled to be there all day. But as the first hour wound down, I already knew the job wasn't for me. I didn't really have the skills they wanted; I wasn't all that familiar with the C/C++ side of the business, after all. I knew more about the Isilon product from the configuration side than anyone outside of field support, but not much about the internals. More than that, the job didn't sound interesting. Java and Swing weren't technologies I was particularly interested in. The office environment seemed cold and unfriendly. The commute was murderous. And I'd just gotten cut from an infrastructure job; why would I want another one?
When the second interviewer came in, I said to him, "I'm sorry, but this job isn't really for me. I think we should call it here."
He looked at me, confused. "You mean you just want to... stop?"
I said, "I'm not going to take the job."
"But..." He stopped, utterly still, for a few moments, then rose and left. A few minutes later, he came back and said, "The candidate isn't allowed to end the interview process."
I told him flatly, "I don't think you can legally stop me from leaving the building."
He stopped for a moment and looked very confused. "No, that's true," he said. "Okay, I guess I'll, um, escort you out."
To this day, I have no idea what he meant by "The candidate isn't allowed to end the interview process." I suspect that what he got from the higher ups he went to talk to was "There's no process for the candidate ending the interview," and went from there, but... weird.