Don't always believe everything, even on certificates, I always keep an open mind, and often ask myself who might have given the information to the census enumerator, or could he even had made a mistake? However, there are major discrepancies about the David on the Bee as well as coincidences so it is doubtful, however, trying to trace that particular David in other censuses hasn't proved successful either, which made me think it might be him.
Nor have I been able to find a Daniel/Danial Bailey in the vicinity of the Trelfa's and strangely enough there is a sad lack of Davids in the area too.
The only other thoughts I have are that maybe he was actually born and registered in Scotland and brought to England/Cheshire at a very young age so that he may not have even known that he was born there, so the birth records there might be worth investigating. I would also suggest that you speak again to the two family sources and ask them to think harder about a name of this laird or whereabouts in Scotland it was and perhaps follow that avenue. I don't know very much about the censuses or information available in Scotland but maybe his mother was working there in 1851 and could be traced that way, or if you were interested enough in the possible father, then if you had a name maybe immigration records could help.
Hope I've given you one or two thoughts even though no facts, sorry.
Mary