He's referring to the voltage drop. If you want voltage regulation as priority, you can't afford a load dependent 0-1.25V drop.
An electronic fuse is perfectly possible, by the way -- but such circuits are quite a bit more complicated than a pair of LM317s. The OP may not be quite adventurous enough to do that.
Incidentally, electronic fuse behavior can be very annoying -- you're connecting a power supply to circuits with bypass capacitors very often, and those capacitors need a lot of charge. Simply shorting an active supply to an electrolytic cap can draw 100A inrush easily, or take milliseconds to charge from around an ampere. Milliseconds is in the range of blowing transistors from high dissipation.
An electronic fuse that opens in microseconds is easy enough to make, and adequate to protect power transistors, but also rather inconvenient to use.
An electronic fuse that opens in milliseconds is hard to make, for currents over a few amperes and voltages above 10 or 20V. The problem is power dissipation in the pass transistor.
Best is both, a limited current of about double what you need for the target, with a modest active period (preferably dependent on voltage drop, so the on-time corresponds to peak temperature reached by the limiter -- maximizing the startup time you get).
The limiter can also be made switching, so that the pass transistor dissipates a tiny fraction of full power, and the dropped power is passed on to something more robust (a resistor or TVS, say), or even returned to the source.
Tim