I was told by someone that the outlets must be with in 24" of the edge of the countertop.
I can find nothing in the 2008 NEC that specifies that. The only thing it says about depth of countertops is that a countertop of greater than 12" deep must get receptacles.

The way I read it was if the outlet was on a wall not directly behind the countertop, the outlet must be with in 24" from the end of the countertop.
Here, you seem to be talking about peninsular countertops? What else could it mean if there were not a wall behind the countertop (other than an island)?

There is a section on peninsular countertops. To the best of my knowledge, the section [which is 210.52(C)(3) ] just says that you need at least one outlet for a peninsula that is longer than 24" long.

That essentially means the outlets must be spaced no more than 48 inches apart.

Sinks and built in appliances like ranges do not count in the 24 inch rule, but you need a receptacle within 24 inches of the edges of the sink or appliance on both sides.

While the peninsula rule is for one receptacle, of you have a long one adding more is a good idea.
Receptacles cannot be face up in a counter either.

One of the real headaches people run into is when window stools are flush to the counter, leaving no place for receptqacles.

While the NEC uses "wall counter space" few AHJs will allow you to skip the receptacles when the window is there.