I think what you heard is based on a misunderstanding, putting the valid point of the different applications Huw described aside.
A jab is primarily a move of control. It controls/checks range, rhythm, and guard position.
Pulling your elbow further back only makes sense if you think that the additional space gives you more way for acceleration and hence more power. Now, this seems to be wrong in four senses:
That's not what jabs are for in the first place, especially in short range.
It opens your side to hooks, which is especially dangerous when you already are in short (= hook) range since they are fast and devastating there.
Power isn't just about acceleration. You also need the structure behind your fist to transfer the power from your whole body into the punch. This is much better when your elbow is in front of your hip/body compared to an arm that hinges only at some pretty extended (and hence weak) shoulder muscles.
It is slow. Opposing directions of movement, the need to build a proper pre-tension through your whole body, etc. And all this for a jab that because of stance can't be as powerful as a cross in the first place?
Thus, I would probably never raise my elbow in short range in the first place. In that range, if what you want is power, you do hooks. And even to set them up, a fast jab with elbow down makes much more sense. You basically do a hook move and waste all the potential power by molding it into some more or less linear move with elbow up.