Theirself is not a word. What you failed to mention in your post above is the source you cited plainly states this. If someone attempts to type the word "theirself" into the search box, he is redirected to a list of the correct words. The word ain't is also discussed and defined on that site in a similar manner. I think we can all agree that our grammar school English teacher would've marked either word wrong on a test.

Here are two links from Oxford and Webster's online dictionaries:

http://oxforddictionaries.com/noresults?dictionaryVe ... »

http://www.merriam-webster.com/dictionary/theirself »

Looks like the Bill O'Reilly word of the day won't bail you out of this one.