I don't understand why you can't get this. It's so simple.
Tyson Chandler is a good player. He's not a great player, nor a top 10 player like you said.
Top ten in efficiency? Sure.
Chandler has such a high eFG% and TS% quite simply because he takes about 90% (and that's actually correct, not an exaggeration) of his shots within five feet. Highest in the NBA. 
Of course he's going to have a higher field goal percentage.
Also, look at his per 36 shots. He averages 7.3. If he got 14 a game and had an offense run through him, would he actually be shooting 70%? NO!!!! Not at all.
He only takes about two shots: putbacks, and pick-n-roll dunks/layups.
If Shaq only did that in his prime, he would have shot 80% from the field.
Also, you love rebounds. Chandler is 27th in rebounding rate this year. For an "elite" player and "elite" big man, that's not good, especially in today's league.