Here is a very good reason NEVER to trust the spellchecker on a PC. :)
Surely human proof readers should be used to spot mistakes like the one in the story. The article implies that human proof readers have been used, but reliance on final proof reading has been left with the PC.
A spellchecker only checks the spelling of the words, and the grammar. What it doesn't check is if the word is the correct one, PCs don't think for themselves. Just try it.
If you put in "it was reigning cats and dogs" the spellchecker would not query it as all the words are spelt correctly, but the wrong word has been used.