If Slughorn knew modifications to the potions textbook that would make the potions better, why didn't he tell students about them? If he didn't, why did he seem to expect that it was possible to get better results than the potions they were making? Wouldn't his potions look just like Hermoine's, given that she was following the directions very literally?
Slughorn probably didn't know about the modifications.
When Harry uses the modified textbook, Slughorn presumes it's Harry's natural skills, not something to do with making the potion a different way.
“But I don’t think I’ve ever known such a natural at Potions!’ said Slughorn, regarding Harry with a fond, if bloodshot, eye. ‘Instinctive, you know – like his mother! I’ve only ever taught a few with this kind of ability, I can tell you that, Sybill – why, even Severus –”
- Harry Potter and the Half-Blood Prince, Chapter 15 (The Unbreakable Vow)