OK
Glamorgan and Gwent are two different counties, so people would not described themselves as born "Glamorgan Gwent" Also Gwent wasn't really used for the area in the early 19th century - it would have been Monmouthshire.
I think the problem may be that a number of people have trees on Ancestry for Edwin, which seem to copy each other and suggest his parents were William and Eunice. I can't see they have any significant sources for this conclusion - although admit as I don;t have a worldwide Ancestry sub there may be info I'm missing. The gravestone only gives dates of birth and death
What I can say as the contemporaneous newspaper reports name 3 brothers, and those and other records place them as being born c1798, c1805 and c1810 - all before William Jones and Eunice Jones of Cwmmera were married. Their locale is also not particularly near Cwmmera.
I wonder if people have spotted his daughter Eunice, supposed she was named for his mother, found a William and Eunice and decided there is a link?
I've just come across this, which is interesting as it's the right parish for the offences. Sadly no age given
Eunice Jones
Father: William Jones
Mother: Mary
Burial 5 Mar 1836, Ebenezer Chapel, Trevethin, Monmouthshire, Wales