Yeah, I'd take CP3 #1 as well, especially if you're playing head-to-head. He led the league last year in two statistical categories (steals being the most rare of the traditional categories), shoots great percentages, and can score and hit the 3.
You could also argue that Amare should be taken before LeBron, for similar reasons: he has ridiculously good FG% and FT% percentages for his position (C eligible), and can score, rebound, and block shots. For his position, he's an elite fantasy player.
LeBron can score, and put up triple-doubles, but isn't all that great percentage-wise. He also plays SF, which is possibly the easiest position to find fantasy production at. Don't get me wrong, I'd take LeBron at #3 for sure. But I think the difference between CP3 and other PGs (or Amare and other Cs) is much greater than that between LeBron and other SFs, fantasy-wise.