I think both of you are correct. If I am setting up a "new" tank for new fish that I plan to get, it's all brand new water. But if the new tank is intended to house fish I already own, I'll fill it up to maybe the 1/3 level with water from their tank, install an already-cycled filter, introduce the fish and then top up with fresh new water. This mimics the sort of water change I would normally be doing, and to which the fish are already accustomed.
I am a firm believer in minimizing stress, and catching a fish in a net to transfer it is already a significant stressor. A new location, new tank set-up/decor, different lighting...these are all changes that are inevitable. I will take pains to minimize the changes that I can, and the water is just about the easiest of these steps.
If it ain't broke...