Ignoring the fact that this is likely 99% false and just a scare tactic someone is trying, I think that it is perfectly fine to hold 2 interviews for the same day in the hopes to trading dates... until a certain time. I think it is definitely a reflection on your professionalism that you cancel at least two weeks in advance or a week and a half at the latest. It's good karma too. Holding on to multiple interviews on the same date and trying to work out trading dates is OK until a certain point and then it's just detrimental to you, the programs and the rest of your future colleagues.
As for the comment on programs themselves having interviews on the same date. While it's not "fair" and you should be able to attend any interview you earned, it's a way for programs to test how willing you really are to be at the program, if you can't even pick it over two or three other programs on the same day, then I doubt they want you to take an interview spot someone else really wants and prioritizes. And on top of that, if every program had a different interview date, I feel like the same top 100 people would be interviewing at 30+ programs and the bottom 400 applicants wouldn't get a single interview, resulting in a ton of residency spots going unmatched on match day. Just my thoughts.
The bottom line: Be respectful and professional and cancel conflicting interviews (or interviews where you realistically don't see yourself at that program for residency) at least 1.5-2 weeks in advance to allow your fellow classmates/aspiring ortho residents the chance to fill those positions. No scare tactics needed.
