in that context it is probably right, but sounds wrong, as it suggesting that he has a right to say things that is equal with the right expressed by the other party. As in specifically relating to the RIGHT.
If you were to say that you have more right to speak than I do, it this is comparing me and you, rather than the right itself.
I suppose you could say that a police officer has greater powers of detention THAN I do,
but I have equal rights of speech THAT a police officer does (I assume?)
But yeah, it does sound a bit wrong doesn’t it? I listen to Radio 4 a lot and find it funny when someone has obviously put a pedantic memo out about something, like the day when all presenters suddenly started saying Eraaaaaan rather than Eran. There is often some strange, but probably correct grammar used!