DH, I hear him and he may be absolutely right. However, I have seen so many guns that "might have been finished by XXX" that were, on careful inspection, apparently finished in Birmingham. I have become fairly skeptical of London makers finishing Birmingham supplied guns. What I would certainly believe is that Robertson ordered exacting engraving and finish specifications and would have returned anything that didn't meet his spec in a London gunmaker's second.
Birmingham work was cheaper than London work. So, unless a gun was made in a slack period to keep staff occupied, there was strong incentive to have all work done in Birmingham. We know for sure that Birmingham workers had the skills to do Boss level best work. It had only to be specified and paid for.
Do you know if the Boss records show these guns as recieved in the white? I've yet to see such a record, but, then, there are still a lot of records I've not seen.
Always open to new information and learning.