There is no excuse for flying someone across the country, using up a vacation day, then fumbling a simple fact about required travel. I'd guess you were more a victim of disorganization than prevarication. This may sound like a silly question, but in my experience many job candidates are hesitant to confront an interviewer over an issue like this. You're very clear about y our opinion that you were lied to. I'm not assailing your credibility or your intelligence.
Interviews can be difficult experiences, but it's very important for a candidate to be candid.
If something seems amiss, ask about it. Someone dropped the ball at this company, and you should have forthrightly picked it up and dropped it into the interviewer's lap while you were in his or her office. They had some serious explaining to do. It's interesting that Personnel apologized afterward. This suggests that someone is paying attention.