It would be interesting to know who had turned you down. I presume from your MBA that you are in the UK.
Certainly McKinsey are or have recently been interested in doctors in The UK. They specifically advertised for them in the BMJ in January. But even then they had a few hundred applicants for 40 places at an open evening, so moving into consulting for doctors in now very competitive.
They don't require you to have a business background or an IT background. It would obviously help with the interview cases to be 'business aware', but you don't need an MBA to get in. IT wise, I don't think that you need to be able to program or anything like that, just be able to use Excel and PP. I interviewed with them and I do not have an MBA and can only do the basics on a computer. The whole process was assessing 'intrinsic' skills, as the previous poster said.
So for a recruiter to say that I would guess that they are either talking specifically about IT consulting, such as the NHS National Programme for IT, or don't know what they are talking about.
I have no idea why you have been turned down without interview. You would think that the MBA would make you more attractive than a lot of other doctors out there. Certainly age may be a factor, although I was interviewing alongside a guy who was 35-40, at least. May well be a CV problem, but you would think your business school would have helped with that aspect.
It might be worth ringing them again to try and find out why specifically you were turned down. Can your business school careers office not help with CV checking and contacts?