I suspect some of the confusion is coming from the fact that everyone has a different time period for budgeting. For us, my DH gets paid weekly, but I'm biweekly. We budget on a weekly basis because the mortgage comes out on a weekly schedule. We can't 100% save the money from 'extra' pay periods because if we did the mortgage wouldn't get paid and groceries wouldn't be bought (as an example :)). Ergo, though there's two months a year where I get an 'extra' paycheck, it can't go completely to savings because those 'extra' two paychecks really aren't extra....they just happen to arrive before the first day of a calendar month, and because we don't have two bills going out on the same day in any given month, it really doesn't matter to us. We just save in smaller increments, on a weekly basis.
I think if you budget on a monthly basis (where a month consists of four weeks), and pay your bills on a monthly basis, it would be entirely possible and a very good idea to treat the third (or fifth) paycheck as a bonus, but any other time period or bill payment schedule, it's just a different deposit date. Not to say one couldn't save the entire thing with planning! After all, you get paid for your 52 weeks a year....
just my two cents! :D