Those "surname meaning" sites are really not to be trusted, and that's putting it mildly. "An outright scam" would be closer. I'm sorry to say that your fellow researcher has wasted his/her money.
For a start, Pembrokeshire is not in "England".
I am pretty sure there is a template that says something like:
"When the ancestors of the {SURNAME} family emigrated to {LOCATION} following {HISTORICAL EVENT}, they brought their family name with them. They lived in {PLACE}. ...In-depth research by skilled analysts into ancient manuscripts such as {LIST OF OLD RECORDS}, shows that the {SURNAME} name was first found in {PLACE} where they held a family seat from early times."
This may be supplemented with random examples of the surname taken from publicly available databases, under the false assumption that all these people are automatically related.
the bit about the "Honour Roll of the Battel (sic) Abbey" can be easily shown to be false:
http://en.wikipedia.org/wiki/Battle_Abbey_Rollhttp://www.nls.uk/auchinleck/mss/barons.htmlThe Ragman Rolls are Scottish, so who knows what a family from Pembrokeshire would be doing on them. Again, nothing like "Stakes" there, anyway.
http://www.rampantscotland.com/ragman/blragman_index.htmThe Falaise Roll:
http://www.robertsewell.ca/falaise.htmlThere is rarely such a thing as a single origin for a surname, unless your surname is very very very unusual. Mine is quite unusual to the extent that many people don't think it's even English when they heard it, and there's still at least three different unrelated groups of people bearing it or it's derivations, because it's a placename-surname and there are at least three places with similar names across the country.
Surnames often come from placenames ("William of Kent" becomes "William Kent", or ), occupations ("Smith"), descriptions ("Brown"), and sometimes patronymics ("Johnson"), so many unrelated people might have adopted the same surname. Some names can be linked to areas of the country (e.g. "Tre, Pol, Pen" names to Cornwall).
Depending on the date your ancestor would have immigrated, consider whether there might have been a military or marine connection (soldiers and sailors are often absent from normal passenger lists but they might appear on other records). Look at who else settled close to him/her, because people often ended up emigrating together with people from the same area, or went to places where they already knew somebody. Think about what was happening, historically, both in England and in the area of the US they moved to, that might have encouraged the move (wars, famines, gold-rushes). Even if there's not a smoking gun in the form of a passenger list, there may be other records you can find.
You can add your surname interests and search for other people researching the same surnames here:
http://surname.rootschat.com/