Another thought occurs:
There is a Robert Jones on the 1851 census, born in Llanelidan, but working as a servant on a farm in Trewyn Bodlwydd. The farm is Caerddinen. I'm wondering whether the registrar misheard Caerddinen as Garthinen ? I'm also noting that both Robert and Margaret were illiterate so they would have had no idea what was written.
I'll try and find out who was living at Garthinen though.