For PayPal Website Payments Pro, CVV is always a required field.
Unfortunately PayPal uses the security code (CVC) only for verification when adding a new card, afterwards all the payments are processed without the CVC code thus a card is verified okay but the payments are always declined. I've tried it many times, it's confusing but these are the rules of my bank (Vneshtorgbank), also it's really unsafe to allow payments without the security code.