Certainly one's standards can be set a bit higher than that
If you are referring to the injuries and the extent of the a/c damage I can assure you that both are directly proportional to height at the point of engine "out".
There are a lot of people who assume that an EFATO occurs at a convenient 500 ft. What a lovely thought! Next time you take off, imagine killing both mags 12 seconds after your tyres leave the ground....