What could be causing my touch lamps to come on by themselves?
This is just a guess...a big guess.  Touch modules work by static electricity jolts. This is why a close lightening bolt can activate them!  I don't know code for amorflex, but check to see if the metal case is grounded properly AND continuously.  My guess (again, a big guess) is the neutral is finding a path to the metal shield someplace besides at the fuse/breaker panel and your static touch is traveling along the metal shield.

One other thought...does the process work in reverse?  Can you touch the floor lamp and turn on the bedside lamp? If not you may have slightly defective module at the bedside table.  If it doesn't work in reverse, switch the touch sensors if you can.  If the problem follows the module you have a module problem.  If it stays at your bedside or the process works in reverse you may have a slight wiring connection problem.  I say "slight" because static voltage goes into the tens of thousands to millions of volts (no amperage that's you it doesn't kill you).  At that voltage, the charge pretty much goes where it wants.  Fun problem.