Another thing, on the Airbus I thought that the fire push button cuts of Hydraulics, Electrics, Air and Fuel.. thus would not allow dry cranking as Checkboard said due lack of FADEC power, but also lack of air pressure available.
Regarding tail pipe fires, obviously it is much better to dry crank the engine and put the fire out. From my understanding, foam and dry powder will essentially destroy the engine. I had one tail pipe fire on A320 at shutdown and had to work hard to convince 'fire one' not to discharge any foam down the engine whilst the captain was carrying out a dry crank (which soon put the fire out). The only indication we had was the ground crew frantically waving at us.
The bigger problem would be if you had a tailpipe fire on engine shut down (like we had) but a non-functioning APU, therefore unable to dry crank. I would think ideally if you could use something non-corrosive to put the fire out it would be much appreciated!
Certainly a tail pipe fire is a different kettle of fish to a general engine fire and it isn't worth destroying the engine in a rush to put the fire out (Fire where fire should be essentially).