The reasoning behind new water in a QT is that the fish already have an issue IN the DT and too frequently that issue is due to the quality of the water in the DT, so why would you want to use more of the same water?I think using water from the etablished tank is fine ... the whole reason for a QT is so you can treat what you have to treat without messing with the main tank. Therefore having the same water could be crucial to helping in the healing process.
Remember to much change to fast could be deadly!!
If a person is keeping up with their water changes, then aside from whatever pathogen is being dealt with, there shouldn't be that much of a difference between new & old water.
You shouldn't have your fish in the position that a water change would be deadly due to a huge swing in parameters....