Maybe the concern is with devices that do not use a neutral, but instead depend on having a small amount of current flowing through the load to keep the device operational when it's in the "off" state. If the current drawn by the LED suddenly drops to zero as the applied voltage is lowered, leaving no portion of the I vs. V load curve to supply a minimal operating current in the "off" mode, then the device might not work properly. Perhaps the LED mentioned by jmellc has such a characteristic. This is speculation on my part, but I can see that this could be an issue with certain LEDs.
Some devices have used the equipment ground as a return path for powering the electronics of the device, but this is limited to less than 0.5 mA by a UL standard. One would think that a timer or photocell could be designed to operate using such low current levels, but I believe there are many devices out there that depend on some current through the load when they are in the "off" state. Dimmers are more challenging without a neutral, because a stable and accurate reference for determining the zero crossings of the AC waveform is desired to prevent flickering.