Slughorn provavelmente não sabia das modificações.

Quando Harry usa o livro modificado, Slughorn presume que é a habilidade natural de Harry, não tem nada a ver com fazer a poção de uma forma diferente.

“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)}}