This explanation is still relevent today, so it is nothing new. I quite regularly use sextants, and although filters do indeed protect the eye, there is another very obvious and common reason to wear an eye patch. The explanation mythbusters stated, although plausible, has no evidence in any historical account. Forgive me for posting this but I just had to add to the discussion. I came across this thread whilst doing a google search. Many merchant ships still carry sextants in case the GPS packs up, and it's still the best non-electrical navigation instrument.

By the end of the 18th century the sextant had all but taken over, and remained in used until it was eclipsed by radio navigation and GPS in the 1980s/1990s. Even after the invention of the sextant various other instruments remained in use, such as the Elton quadrant, a post-golden age development of the backstaff. During the golden age the principal instruments in use were the backstaff (or Davis quadrant), cross-staff, and quadrant. The invention of the Hadley Octant in 1731 and the Campbell Sextant in 1757 reversed the process and the navigator once again had to look at the sun, but these instruments were fitted with multiple dark-glass shades to cut down on the danger.

At around the same time the cross-staff underwent some modification so that it too could be used to take back sights. John Davis is usually credited with the invention, but there were others working on the same principle at the same time. The earliest instruments designed specifically to take a back-sight (ie, with the sun behind the user) were developed at the end of the 16th century. The earliest navigational instruments such as the quadrant and cross-staff required the user to look at the sun, but even the astrolabe could be worked using a shadow rather than looking direct at the sun. As Dave said, the sextant (as we know it) was not invented until after the golden age of piracy.

Patch age of pirates