You have to justify any claim you make. The burden of proof is upon the one making the claim, whether that claim is a positive or a negative. As such you made the claim that those who voted to leave had no genuine grievances with the EU. Are you going to support that claim? The time you don't need to support a negative is when the negative is the default position. Given that 52% of the country voted to leave, the default is surely that they DID have genuine grievance, or at least felt that they did. You, by asserting otherwise, are going against that default - so whether the claim is expressing a negative or not, please support it.