I'm not a medic, so I won't be as informed as others on this thread, but I think that the comparison made between medicine and maths was not fair. The point the poster was making was that if you had 10 A*s, bio and chem (+ 3rd science if applying to Cambridge) at A(*)A(*)A(*), relevant work experience, 850 UKCAT and 21 BMAT, you could be rejected by having a bad interview and/or applying to the wrong universities, whereas if you had those other conditions you would definitely get into maths at Cambridge. Like I said, this isn't a fair comparison to make.
First of all, the maths applicant has applied to the right university, Cambridge, whereas the assumption is that the medic has not. Whether you have SSS for maths, or 995 in the BMAT for medicine, they would both put you in an equally excellent position, IF applying to Cambridge. Obviously if you apply to uni who ignores UKCAT/BMAT, outstanding scores won't boost your chances, but then the same could be said for maths. Oxford don't look at STEP.
The second possibility for four rejections is that the med applicant has weak interviews and fails to sell himself as med student. A maths student who failed to sell himself through the PS and any interviews would also get rejections.
Medicine is a tough subject to get a place for no doubt. It is the subject with arguably the largest set of admissions criteria. Since it doesn't matter which med school you go to, the key is knowing which schools to apply to based on your strengths and weaknesses. What I disagree with is the suggestion that it is the only subject where you can get five rejections. For example, if you apply for economics, my subject, and go for the top 5 or 6 universities (the ones which I would say are on par with medicine in terms of general prospects), it is very easy to get rejections for small things, since they have 15-20 applicants per place.