The next question is whether there truly is a problem with wires smaller than #14 on terminals - e.g. wire can end up beside the screw rather than under it - or whether the minimum is simply based on the NEC minimum of #14 on 15A circuits, with no one guessing that a breaker might be used to power a short tap to an in-panel device. I would assume that on a screw terminal designed for #14, #16 would also be safe - the diameters are not that different.
Another consideration is whether the wire will carry enough current to trip the breaker in the event of an internal short circuit. (The wire may overheat with a continuous 15A load, but there is no risk of that with a dedicated single device on the wire - only a short.) #16 wire has a resistance of .004 ohms per foot. By my calculation short circuit current on a length of ~8ft of #16 wire is in the thousands of amps, meaning that any size of household breaker would trip in the event of an internal short, well before the wire got hot enough to start a fire. I assume this is why smaller-gauge taps serving individual devices are permitted in the NEC.