My Dad is convinced that the "textbooks" are among the worst things to happen to parenting.
And you're right...potty training doesn't WORK until the kid himself is ready and doesn't wanna be wet! We all trained at varying ages. The girls learned earlier than the guys, on average, and some of the guys learned pretty late because they just didn't give a darn.
When our first was about a year old, I had a mom and her son from a playgroup over for a visit. She said she was fixing to start potty training her son, who was the same age as our Paul. She said her Mom told her it would work. I told her SHE might get potty trained, but I doubted that her son would be. I don't think she liked that.
All four of ours trained at different rates, but three years old was the earliest for any of them. Joseph was the slowest. He knew what to do, he just didn't want to do it!