Someone will correct me if I'm wrong (DJPil?), but I'm pretty sure that take-off safety speed is a uniquely Australian manifestation probably going back to the old DCA. It used to be in the old uniquely Australian performance charts, but I' can't recall ever seeing it on a manufacturers chart.
Pretty much how I understand it.
Take Off Safety Speed? The manufacturer states this is the minimum speed until 50' to ensure controllability of the aircraft in the event of an EFATO.
The lift off and 50 foot speeds are purely performance related, ie, you must attain these speeds to achieve performance.
The only mention of a safe speed with regard engine failure is usually found in section 10-Operating tips, of a Piper manual. For instance the the Arrow III states, Section 10-10.3 (b); "The best speed for take-off is about 70 KIAS under normal conditions. Trying to pull the airplane off the ground at too low an airspeed decreases the controllability of the airplane in the event of engine failure"
Considering the lift off speed flap 25 on the chart is max weight 59 KIAS (62 KIAS at the barrier) and the stall speed is calculated at around 55 KIAS full flap at max weight, this is not 1.2 x the stall.