How to replace an anti-siphon spigot without access to the back end?
You'll have to cut the drywall.  Honestly if I were building the house I wouldn't do something special for this either.  I'd just drywall overtop and if there is a problem the guy replacing it can add an access panel if he wants.   It isn't any easier to do it at build stage than repair stage and you delay the additional cost for how ever many years it takes before it breaks.  Also chances are if it breaks and floods like this the drywall above around it will be damaged by the water so even if you did access panel it you'd still be looking at drywall repairs.  This sounds like a finished basement so I don't even see a significant advantage to an access panel given how often these things have to be replaced.  

I do prefer to do a yard butler instead of house mounted hose bibs though as you can place them anywhere without trip hazards and they should be easier to replace and if they fail they don't damage your house.