Thanks PA, appreciate your explanation
In their own books, the FAA generally explains the hazards of attempting to turn back to the runway if you have an engine failure on take off. However, they also say this:
Quote FAA-H-8083-3A, Airplane Flying Handbook
Concerning the subject of turning back to the runway following an engine failure on takeoff, the pilot should determine the minimum altitude an attempt of such a maneuver should be made in a particular airplane.
As I said, it is all about knowing your airplane. Some will do it and some will not.