Is it true that it has been authentically narrated from Ibn Abbas (may Allah be pleased with him) that he said one should not pray Jumu'ah and Dhuhr if Eid falls on a Friday, or is this statement refuted? And what is the evidence for that?

Whoever attends the Eid prayer is granted a concession to skip the Friday prayer. However, whoever does not attend Eid must attend the Friday prayer. The Imam must hold it so that those who did not attend Eid, or those who attended Eid but still wish to attend the Friday prayer, can pray it. And upon those who are granted a concession to skip the Friday prayer, the Dhuhr prayer is obligatory. The opinion that it is waived is weak, because the obligatory prayers are five, and because when Ibn Az-Zubair did not go out for Jumu'ah, they prayed Dhuhr individually, and Ibn Abbas approved of that. The opinion that Dhuhr is waived when Eid and Jumu'ah coincide is incorrect and has been abandoned by scholars for contradicting the Sunnah. It is more preferable for those granted a concession to skip Jumu'ah to pray Dhuhr, and if they were to pray Jumu'ah to avoid disagreement, that would be even more preferable.