Well they've told me that as long as you have the passes they state on the web you're ok. At the end of the day if they were going to filter academically they'd filter at alevels which matter more, so their offer wouldnt be AAB, it would be AAA, which it isnt.
The thing with medicine is that no matter how good you are, or your ps is, at the end of the day its luck. Most applicants will meet all requirements and will have brilliant personal statements, but there's no way everyone can be interviewed. Obviously no uni is going to say "you might be fab, but its down to luck really". Have another try as Kings is fantastic as a uni, or at least it is in my opinion and maybe you'll have better luck.