I think those pictures epitomize why Tesla are concerned about 13A charging. Would be terrified to see the wiring behind that, and what does "20A, Lamp load 10A" mean? :scared:
"Lamp load" refers to ordinary incandescent lamps, which take a huge current surge when first turned on, and hence are quite aggressive to the contacts of the switch used to turn them on. It is good practice to use a switch of higher rating than the total operating current of the lamps.
Since timeswitches are quite commonly used to switch lamps, the manufacturer has specified a specific limit on the amount of lighting they recommend to be controlled with their switch, rather than leaving it to the electrician's judgement (or requiring him to look it up in a datasheet).
Fortunately, the Model S is the complete opposite of a lamp load - it starts low and gradually ramps up the current, so is quite kind to switch contacts.
On the other hand, I have to agree that I'd think twice before using such a circuit for charging unless I knew what it was originally intended for.