I have to say, I never had an issue taking anybody's photograph during the years I lived in Dubai, though that may be because I generally asked first. At any rate, there is no hardcore religious reasoning behind it that I'm aware of. The Bedouin people, in common with many 'primitive' societies are very superstitious, and as such believe that when you take a picture of them, you are stealing a small part of their spirit. Though many of the locals of Dubai are descended from the Bedouin tribes, I very much doubt that this was the reason behind their displeasure.
I thought it might be interesting to expand on the phenomenon of Russian '"tourists" as mentioned by seanni. It used to be (and to some degree still is) true that the United Arab Emirates, Dubai in particular, were regarded as a kind of candy store by those fortunate enough to emerge wealthy from the Soviet Republic's collapse.
The procedure was simple, effective and has a certain air of genius about it (at least in my opinion). These people would hire an aircraft from the dispersed fleet that used to be Aeroflot... and fly it to one of the many small airports in the UAE, notably the ones at Sharjah, Ras al Khaimah and Fujairah. They would then park these aircraft on the apron (the tarmac area by the runway) for up to a week - something completely unheard of in the Western World, where you have to keep your aircraft in the air for it to be profitable. Indeed, it's so unusual that the (somewhat better) airports at Dubai and Abu Dhabi can't provide the space for such activity.
These people then hit the nearest Souq (Arabic for 'market') and buy up so-called 'white goods' (refrigerators, microwaves, dishwashers, ovens) at impressively low prices. These are then repacked like Russian Dolls (a microwave inside a small fridge inside a large fridge, etc.) and loaded into the aircraft.
The consequences of this particular type of import industry are often overlooked, but quite pronounced nonetheless. Essentially, there was a fairly substantial boom in the traffic at the minor airports and the sales at the Souqs... not to mention in a particular type of accommodation in such areas. Even though the crash was predicted several years in advance, there were still opportunists who invested quite heavily, building special blocks of apartments/storage areas that were almost completely geared towards supplying the demand of the "tourists".
So when in around 1998 the Rouble crashed hard, and the people who had fuelled the industry lacked the disposable income to continue, the bubble burst. Profits in the Souqs fell, and there were a fair few complaints... but not a lot that could be done. The minor airports have fallen into disuse, though I believe they're still open.
In recent years, the manufacturers of the 'white goods' have established their own distribution centers in the former Soviet Republic, so the demand has fallen sharply. This, combined with the economic crash has caused the practice to become increasingly infrequent... though it certainly continues.
And to add a little end-note to this decidedly dry and boring writeup, Frankie sent me a message or two detailing a compelling explanation of the whole photography issue. Islam forbids idolatry... and what is a photo but a potential icon? All traditional islamic art is calligraphy, for this reason.
But hey, I can't stress this enough. If you want to photograph somebody, ask their permission first.