Vendor insisting that a payment is pending

We are a start-up and we hired a web developer to work on our website. In the quote that he gave us included the website development rate and annual maintenance service. This payment was made in 2 installments as verbally agreed upon. This April is a year since the website was hosted. We found him fairly non-responsive to our email to make certain updates. After repeated follow-ups and an indication that we wanted to change the vendor, he came back with this - we had a pending payment for Email and Support services amounting to 10,000 from Feb17 to Feb 18. To our knowledge all payments were made. There is one point in the terms that states - Cost of materials such as Hosting, Emails, Stock pictures are not included in the quoted price but calculated after the selection. But no invoice was given to us or anything else to indicate that such a payment needed to be made. All payments for which an invoice was given have been made. My question is can he make such a claim without having even given us an inclination that the amount was due. How do we respond to this?