First question is are you sure this is fro an adsense account not for Adwords (ie ads you pay for)?
It looks legit to me (had one myself as I was expecting it) although it was for Adwords not adsense. If you originally register saying that the ads are NOT for "business use", they will charge you VAT, however if you later tell them that they are for "Business use" after all they will refund you all the VAT you have paid to date and leave it up to you to sort out with the VAT man. If you are not registered for VAT the money is yours to keep.
It says on the covering letter refund is from january 2004 so google think you have had the account since 2004. Could it be that you had an old account and have just registered a new one and they have in some way tied the two up and decided you are due a refund?
Edit - Just seen read your second post. Almost certainly it is the Adwords account if you have one, you can presumably check the account number?
Dave