Playing the devils advocate;
1) If the AME isn't VAT registered the customer doesn't pay VAT, (if it's a sideline to your main medical activities, which it is to quite a few AMEs you'd have to work very hard to reach the VAT threshold each tax year).
2) If the AME is VAT registered, he can claim the VAT back.
3) It's a commercial service provided by a professional service provider, as with any other service provider, if the turnover meets the threshold, why shouldn't the appropriate VAT be applied.
4) Professional fees and such expenses can be offset against income tax, check with an accountant, the IR or when you fill in your tax return.