FWIW, this turns out not to be true in many cases.

For one thing, a drop-bar road bike -- particularly a touring bike fitted to the rider -- can be set up so that the handlebar height is at saddle level. This yields a riding position when the hands are on the tops of the bars that's not much different from a hybrid. But the options of going progressively more "aero" by moving forward to the hoods or down to the drops are still there.

For another, depending on what might be ailing your back, the posture on a road bike may stress it less, not more, assuming the rider bends properly at the hips rather than arching the back. Road bike posture allows the rider to distribute his weight more evenly, rather than having all his upper-body weight supported vertically through the spine to the saddle.

Personally, I have arthritis in my spine, and switching from a hybrid to a road bike helped a lot.

RichC