It's ridiculous to think this doesn't/wouldn't make a difference, unless you're applying from a top school.
Put yourself in the program director's position. You have 5 spots, 500 applications, and 50 interviews to give out. Do you really think that a program is going to interview more than 1-2 kids from the same school? Interviews are a zero-sum game, for everyone 1 person you invite you can't invite someone else. No one is going to allocate a heavy % of their scarce interview invites to get a bunch of kids from a random midtier. There's just no gain or reason for them to do that.
I've seen this in action at my school the past few years. They'll have massive #s of applicants apply lets say Derm/Ortho/Plastics/ENT depending on the year, and the match % is horrific. Let's pretend its 10 applicants to ortho. Typically the top 2-3 (High 250s, great research, AOA, etc) applicants get 10 interviews, then all the regulars (250s, some research, +/- AOA) get split pretty terribly and get maybe 4-6 interviews, and the remaining poor applicants get almost no interviews except for home and aways. The top applicants almost always match and about half the good ones match, and the bottom of the pack almost never match. Match rates vary (I'm estimating) at my school between 33%-75% overall by year and specialty.
Also when I talk to upperclassmen, last cycle and this one, almost no one has gotten duplicate interviews that aren't in the same state or very close by. I knew two exceptional candidates that matched a competitive specialty and each one had 8-10 interviews and even then, the only overlap was the home program. Also almost all of the average candidates who apply match at a home or away.
So yes, if you have high numbers like 20 people applying ortho, 15 derm, 1o plastics, 6 vascular, etc it just won't be good overall (unless you're Harvard Medical School) as you're splitting the interviews between a bunch of homogeneous candidates.