Three years ago.
You're assuming all the rooms in use, at full capacity, and everybody visiting the parks. Rooms are closed for renovation, repair, cleaning so not every room can be occupied. There may be only one or two people staying in a room at a time. People staying onsite don't always go to a Disney park everyday they are there, they may take the day off to rest, may visit one of the waterparks, or go to another area attraction.
A resort may have no rooms left at times but I doubt every single Disney resort will ever be fully booked at the same time. I also do not believe Disney reservations has access to all the rooms in a resort. Blocks of rooms may be reserved by places like Expedia or for other reasons and thus cannot be reserved by Disney reservations.