BoTRK simply works very well on Zed.
Contrary to popular belief, Zed doesn't magically avoid enemy attacks with his shadows on a .1 second cool down. The Life steal from the build path gives him some sustain against ranged poke.
Around level 6, Zed would be able to upgrade for a Cutlass. The stats may seem mediocre, but it is really the active that benefits Zed. With a cutlass active, enemies won't be able to run away from Zed after he Death Marks them. The speed boost also allows him to sneak a few more AAs in during the duration before the enemy gets too far.
The passive and active of BoTRK in general makes up for the weaknesses in his kit. It gives him sustain, synergizes well with his ult, and lets him deal with Health Stacking tanks that would otherwise counter him.
Of course, there are other alternatives. One can opt for a Hydra for example. For those who play AD Casters frequently, and can cancel their AA animations with the Hydra active, Hydra gives Zed unparalleled burst. It gives him kill potential without his ult with a combo of: W, E, W, AA, Q, AA, Hydra, AA. Additionally, it lets him push waves without using W.
Another option is to simply rush full damage and LF and build BT.
Players who reports you for not building BoTRK on Zed simply don't understand his kit. It works well on him, but it isn't always necessary. Especially against another assassin in lane, Hydra will save you countless more times.