I'm sure I asked questions like this too.....
Now realize that this is only my opinion and by no means gospel, but I believe this to be true and hopefully it will help.
The reality is that there is no true answer to this question.
Rotating can get you an interview (but rotating can also get you uninvited from an interview that you would have gotten based on your record alone)
Great board scores can get you an interview
Nothing guarantees a spot at your top choice...NOTHING(unless your dad is the chairman)
Obviously rotating is better than not but people match every year at places they didn't rotate. This includes HSS, Harvard, Duke, Pitt, UWash et al.
The better your application, the better your chances of getting an interview, but even this is a crap shoot. The top programs are idiosyncratic about who they interview and sometimes it has nothing to do with your academic credentials.
Lots of people rotate.....lots....so while this does put you in a more rarefied group come interview and rank list time, it is no guarantee. There are large committees that meet and discuss all the applicants, and usually you only rotated with a select few of them. So decisions are made more based on interview day info, letters of rec and other mysterious factors that I have yet to comprehend.
Being a cool, humble, modest, outgoing, awesome, interesting and ENTHUSIASTIC individual on your interview day is by far the MOST important and BEST way to get a spot.
The be all and end all is that there are a LOT of great programs, there is no No. 1 program but there is a 'best' program for you based on what you want out of your life, where you want to be, who with and so on.
HSS is not better than Harvard, Duke, Jefferson, Rush, UMich, CarolinasMC, Ohio State. It is just different. Some people couldn't even imagine living in NYC and think the program is overrated anyway. Others think it is Mecca.
If you are lucky enough to get a spot, be happy that you get to live the dream of doing Orthopaedics every day. Where is really immaterial.