I don't think this is much better. I wouldn't work for someone who asked me this question, even if this were the rationale. Who knows why someone would divulge their password. I bet there are reasons other than being completely devoid of common sense.
Regardless, I bet that any predictive relationship between willingness to divulge a Facebook password in an interview and the ability to perform adequately as a software engineer is weak at best. To me, an employer who doesn't understand that shows poor capacity for unbiased reasoning.
If I were interviewing a candidate and had decided to ask this question, my response following their reaction would be "Just kidding. We don't do that here" followed by taking note of how concerned they initially appeared at the question.
The "just kidding" would probably need to be before I answered. If I start to get up and walk out and then they say "no, I was just yankin' ya!" I'm going to be really suspicious.
What exactly do you think their level of visible concern would tell you about them? An employer conducting jokey personality tests would be a huge red flag for me.
Regardless, I bet that any predictive relationship between willingness to divulge a Facebook password in an interview and the ability to perform adequately as a software engineer is weak at best. To me, an employer who doesn't understand that shows poor capacity for unbiased reasoning.