Yes, it makes perfect sense, and I've been caught out by this one persoanlly in my career many years ago. I vowed it would never again happen to me.
It isn't an issue for HMRC - it is your employer that has fouled up. Your employer is wrong to say you have to deal with it via HMRC - they can do nothing. They only work on what the employer tells them you have earned in what year (via the monthly returns they make to HMRC and then annually in a thing called a P14 - which is a return they make to HMRC annually for each employee). The same data as is on the P14 appears on your P60.
Unfortunately the deadline for your employer to make their annual return to HRMC for the year 2008/9 is the 19th May - so it is very likely their return has now gone in. In case it hasn't, do it tomorrow!
The return cannot easily be reversed.
Sorry but I don't hold out much hope - unless someone else knows different?