The wires that they are referring to as rotted at the transom or the drive are the wires that connect the trim limit switch (sets upper and lower limits on travel of the drive) and/or the trim sender (sends position signals to the gauge on the dash). Those can be completely bypassed, if one wishes, and the drive will still function. Without the sender wires, the gauge simply won't work. Without the trim limit wires, the travel of the drive up and down is a function of whether the pistons are full extended or retracted.
The trim/tilt function is controlled by a hydraulic system that is more or less independent of those rotted transom/drive wires (excepting when the trim limit switch kicks in). It is not an uncommon practice, when a trim limit switch fails, to just jumper the wires past it. This allows the drive to raise and lower fully from either the trailer/tilt button or from the trim buttons. The only downside of this is that, when using the trim feature, you have to be careful not to raise the drive too far while running. Otherwise the U-joints start to protest...