Do experience buffs affect skill books?

I always assumed that Skill Books, Trainers and other free skill boosts always gave you exactly 1 skill level. However reading about trainers on the wiki I see that:

Training benefits from Sleeping and Standing Stone bonuses, though the XP so acquired will never result in advancing more than one level.

The same is also true for the free skills boosts.

So now I’m wondering if the same is true for skill books as well?