So, back in my 1e/2e AD&D days, my campaign worlds were always very fluid. Part Forgotten Realms, part Greyhawk, part Dragonlance, part my own shenanigans, hell, there were even some Dark Sun elements in there. But they were the parts of the settings that I liked, so even the players that knew the settings better than I did couldn't run roughshod all over the place (not that I was being adversarial, but I may already have had an evil organization trying to take over the world, so the Zhentarim might not have existed, for instance.)
I think you were well within your GM Agency to say no, however, in the interest of the rule of cool I would have said, "Yeah, totally, Waterdeep is a huge city on the other side of the sea. However, GM to player, keep in mind that this game isn't set in the Forgotten Realms, so you might see some differences in this Waterdeep from what's been published."
Of course, YMMV. 🙂