The purpose of this poll was to help dungeon designer to get an idea of what people actually got as as dungeon tiles. The poll's result give you now an idea of what you should or shouldn't expect your players to have.
A minority of people owns the modular dungeon board system from Dungeon & Dragon (Parker/Hasbro). In addition, a small minority of people also own modular D&D tiles and battlemaps.
So in conclusion : when you design a quest, don't be afraid to ask people to print custom tiles as long as they add something up to the quest.
The fact that people own modular D&D tiles could also mean that people like to play with a modular dungeon system from time to time because it help changing the gameplay.