Why does this two's complement shortcut work?

It works because adding one to a binary number is accomplished by flipping all 1s to 0s from the right until a 0 is reached, flip that to 1 and stop (essentially carrying the overflow of adding 1 to 1).

So one method flips only the bits to the left of the first one, while the other flips all bits, then flips the first 1 (now 0) and the bits to the right of it back.

e.g.:

 01000100
 10111100  // copy bits until a 1 is reached, then flip the rest

vs

 01000100
 10111011  // invert all bits:
+       1  // add one
 10111100