Correct. The first invert comes from simply rotating the polarization film 90 degrees. A polarizing film should come with the backlight, you remove the original one when you remove the reflective backing off the LCD glass. Bam, colors inverted, that simple.
The second invert (giving you back "normal" colors, but at a higher contrast ratio) comes from soldering a bivert chip to the pcb. This can actually be a bit more dangerous than many people make it out to be. It's more difficult on a gameboy pocket. I've lost a few gameboy pocket internals because of a bivert attempt (maybe 20%?) It's no HUGE loss, as I just use the screen, buttons, case, etc in another system. It's all easily put to use.
Usually the problems arise when disconnecting the traces on the pcb, or (most often?) the bit more jostling around inside the system causes LCD failures somewhere else from a tweaked LCD ribbon cable.
But I suppose that's the risk from any mod, especially on something so old with fairly fragile internal components.