He might mean he claims the total invoice amount, including vat as an expense against income tax, which is correct if not vat registered. There's no 'claiming back' anything if you're not vat registered.
If you are vat registered, you actually do claim back the vat you've spent on business expenses. That amount is deducted from your quarterly VAT bill. If you have not received as much VAT from customers as you have spent, then HMRC will send you a cheque for the difference. So in that sense, it really is claiming back.