The first to pick up this strange distinction is MAA 134: Battle for the Falklands (2) Naval Forces. Even though parts 1 and 3 of the mini-series feature artwork, this book went for a photograph of an aircraft carrier. The reason for this is pretty simple - the book doesn't contain any artwork, just colour photographs of the naval forces.
The second book is a bit more of a mystery to me. MAA 279: The Border Reivers has a cover photograph of a big helmet. Yes, it is a very 'reiverish' helmet, but this book contains some of Angus McBride's best work. I'd like to have been at the meeting that made that decision, but, alas, it was before my time.
The final, and by far most recent addition to this short list of Men-at-Arms cover oddities is MAA 432: Japanese Special Naval Landing Forces: Uniforms and equipment 1932-45. At first glance it looks like a classic Men-at-Arms title, with the three figures. However, these figures are actually photographs. In this book, all of the 'figures' are actually photographs as this was deemed to give a better example of the uniforms of these soldiers. There is a bit of artwork in the book depicting officer insignia and the insides of helmets.
At the present rate, you should look for the next photographic Men-at-Arms cover around number 600 in the series.