I'd suggest that they'd want/need to do additional fraud checks because you were ordering with a card registered to one address and then despatching to another. I'm not sure of that though, but it kinda makes sense to me. I'd doubt they can simply request your bank phone you or anything though, its up to your bank to carry out its own fraud checks rather than PCS requesting they do. I think that's separate.
It makes sense to me too but if you can't do them in 3 or 5 working days then I think that's pretty poor customer service. PC World, when I ordered an external hard drive a few months ago in their online sale phoned me when they saw it was 2 different addresses just to clarify what was going on with the order and that was that.
I'm a bit torn now about what to do, as one of the above posters said PC World off the rack doesn't compare to something custom.