As my wife is one of those Chimps that don't do sums correctly (a hoot at parties), I can tell you that the majority of calculations have been conducted incorrectly over many years - but the new HMRC computer system, installed two years ago, is now showing up these miscalculations and is correcting them.
Luckily, the system can only go back a couple of years (rather than the revenues preference of 9 years) and those errors found have to be rectified before the true figures can be calculated.
Even for me, this showed that I had a 9K bill last year and only several hundred refund this year. Believe me, my missus went through those bills very keenly, but couldn't fault them.
Pensions and not notifying the revenue of changes are the most likely reasons for bills. (obviously the revenue wont ever say it's their fault - so it must be yours!)
If you don't understand the Statement - there is a number on the top of the accompanying letter that you should call - not some mates "friendly" number. They should only redirect you to the right office.