Assumed thrust method: ATM IS NOT considered a limitation.
Derate IS considered a limitation.
I believe this has to do with Vmcg. ATM is not considered a limitation because Vmcg is derived using actual OAT. So even if you increased the thrust during take-off and lose an engine, you should still be able to maintain directional control (so long as you do not increase above the rated thrust for your take-off, ie TO or TO-1).
In the case of de-rate. Let's say Full rated thrust (TO) of the engine is 50,000 lb and de-rated thrust (TO-1) is 45,000 lb. The Vmcg for using TO-1 is derived using 45,000 lb thrust. Now if you have a take-off situation where V1 = Vmcg using TO-1, and for some reason you decided to firewall the engines at V1 and happen to lose an engine, directional control will not be assured with full rudder. This is because Vmcg for TO is higher than Vmcg for TO-1.
So this brings me to another question. If you take off using TO-1, and you encountered "Windshear! Windshear!" at V1. What will you do? I was thinking that on contaminated runways or other situations when V1 was reduced, the V1/Vr spread is larger and the exposure to this scenario can be significant. Are my worries without a cause?