Thanks for the link! LOVED your post over on TwityPuzzles.com - not only the detail on parity, but the humorous way it was written. I registered and am currently awaiting with baited breath to see if I shall be "approved" by the gods of that site to be worthy of membership!
I will post a pic the next time it happened, by Murhy's Law of Cubing, it will probably never happen again now!
However, I have since learned a second way to solve, and have discovered if I just switch methods, it seems to work.
If you are curious, I will explain. If not, just click away now, and you are free to roam about the Internet as you were previously before I briefly interrupted whatever you were doing. (a tip to your post)
I learned to solve: 1st 2 layers, cross on bottom, line up bottom center edges, then solid bottom, then permute corners, which is when I get the above issue at times. I just learned that Patrick Bossert, the 12 year old who solved the Cube and published the first book and sold 1.5 million copies in 1981 did corners first - so I learned his method: 1st 2 layers, cross on bottom, (skip: line up bottom center edges) then solid bottom, then permute corners, finally permute center edges.
Still deciding which I like better, but when I get "parity" (or should I say, "apparent parity"?) I just switch to the other method and it seems to self-correct.
Loving that all this help is available and amazed that I solved this myself as a kid.
Wrote about it here, in my Leadership Lessons from the Rubix Cube: http://kidology.org/rubixleader