VAT query on a charge refunded

Hi. I am new to this but hope someone can answer my query.

My company have received incentive income from one of our service providers - they provided a self billing invoice for this. We were then charged an amount for business throughput shortfall - they provided a vat invoice for this. Both the incentive income and the shortfall charge were subject to VAT which we treated in the usual way.

The service provider then agreed to waive the shortfall charge and has refunded us the net amount, but not the VAT charged. I queried this and they have stated they are unable to refund the VAT and I can claim it as input VAT in the usual manner.

Is this correct? I can not find anything on the HMRC which covers this.

Many thanks

Karen