I wouldn't worry about what the books say hun - chances are your little man hasn't read the book either

Some kids genuinely need less sleep than others, just like some adults need more or less sleep than others. DD dropped her day sleep most days by around 3, other days during our "hours quiet time" she'd nod off and have a little nap, it really just depended on the day and what we'd been up to (ie, how worn out she was). After lunch would be quiet time, where even if she wasn't asleep she was semi-resting by either watching a movie, playing quietly in her room or reading a book - just a little down-time to recharge.

If an afternoon nap results in skylarking off the walls till silly o'clock, I'd be dropping it personally. Good night sleep is definitely more important