Cadarnhaodd Arweinydd y Tŷ ar 7 Mawrth, wrth ymateb i gwestiwn am Banel Dyfarnu Cymru, nad oes gan Weinidogion Cymru unrhyw ran ym mhenderfyniadau'r Tribiwnlysoedd, a wneir gan aelodau’r tribiwnlys ar sail y dystiolaeth ger eu bron. Mae mesurau diogelu eraill yn eu lle i gynnal annibyniaeth farnwrol Tribiwnlysoedd Cymru, gan gynnwys mynediad at arbenigedd y Swyddfa Ymchwilio i Ymddygiad Barnwrol. Ceir darpariaeth yn Neddf Cymru 2017 ar gyfer Llywydd Tribiwnlysoedd Cymru i gryfhau arweiniad ac annibyniaeth y farnwriaeth ymhellach.
On 7 March the Leader of the House, in response to a question about the Adjudication Panel for Wales, confirmed that the Welsh Ministers have no role in decisions of the Tribunals which are determined by tribunal members solely on the basis of the evidence before them. Other safeguards are in place to uphold the judicial independence of the Welsh Tribunals, including access to the expertise of the Judicial Conduct Investigations Office. The Wales Act 2017 makes provision for a President of Welsh Tribunals to further strengthen judicial independence and leadership.