Snape: *finds better ways to make potions than the textbook at 16*
Snape: *decides not to teach students except what's in the book*
Actually, there is not a single time that we see Snape tell students to open their books and follow the recipe. What he does do, is put a Potion recipe on the board himself. With these recipes, Hermione makes perfect Potions for five years. Suddenly, in Year 6 she has Slughorn, a teacher who *does* make the students use the books. And just as suddenly, she can't make perfect Potions anymore. No one can except Harry, who is using Snape's old text.
The explanation that fits these facts is that Snape does share his improvements.