HerHusband presented the following explanation :
The LED itself regulates voltage. That's what a diode does.

http://www.merriam-webster.com/dictionary/diode
an electronic device that allows an electric current to flow in
one direction only

It has been many years since my electronics days, but I believe a diode
does have a fixed voltage drop. I think it's around .7 volts if I remember
correctly. So it does regulate the voltage in some respects.

Yes, that is a forward voltage drop across the junction. The voltage
depends on the materials used in the device. The regulation function of
a diode is usually a reverse voltage taking advantage of the breakdown
characteristic. IOW a reversed diode as a shunting device. The same can
be used as a reference diode to control a transistor regulator. Zener
diodes come to mind for this.