The idea is to have a ground path with the least resistance. The 3' rule is really just an arbitrary number that was essentially pulled out of the air.....no real basis for that specific length.
But the general idea is that the "wire" used for the ground from the amplifier will generally have more resistance than the chassis/body of the vehicle. So in order to have the least resistance, you would want to have the higher resistance medium (the wire) as short as possible and utilize the lower resistance medium (the chassis/body) as much as possible.
However the chassis/body can be a very poor conductor in some vehicles, which makes the use a dedicated ground wire back to the battery a better option. Also some people run large enough ground wire that the wire's resistance might actually be less than the resistance of the vehicle's chassis/body, even if it's a reasonably good conductor (as far as chassis' go). I've seen conflicting reports on the resistance of vehicle's chassis.....some state it's equivalent to ~17' of 2/0ga wire, others state it's equivalent to ~17' of 4ga wire.....and both were reliable sources. But regardless, if the wire itself has less resistance than the chassis (i.e. if your vehicle's chassis is equivalent to 17' of 4ga wire in resistance and you are running 1/0ga wire), it's a better choice to run the wire directly to the battery.