Try to think of deadlifts as lifting with your back, but in a controlled, symmetrical and familiar manner.
Generally, back injuries don't arise from simply lifting with your back. Problems arise when you lift something large, unwieldy, and unstable.
A bar's weight is symmetrical around your lifting position. If the symmetry is ruined, and you try to maintain the lift, certain muscles will have to over-compensate, and this can cause extreme strains.
"Real-life lifts" are more likely to be unbalanced, and asymmetrical. Things can break, and fall apart. Drawers can slide out, contents can shift and drop.
Imagine if you're doing a deadlift with a bar, and half-way through the lift, someone removes a plate on one side of the bar. That is problematic! And the analogy is more likely to happen outside the gym.