Pre 1865 all information (as far as I can determine) was taken solely from Mathieson (with virtually no acknowledgement - even the words are his with just a few minor changes - compare the book with his paper), however she did not fully check things out so there are several errors, though your quote may well be correct - 1831 can only be from a newspaper advert (Mathieson would give the issue if it was) as no directory until 1837 - I thought I'd gone through all those + the card index to the newspapers, also done by the indefatigable Mathieson, upon which he drew heavily, when I put my pages together - nor did she appear to do any personal research on 19th century pubs though the 20th century material may well be hers.