I have this 1951 Hamilton 917 in a factory Wadsworth case with a rubber stamp code.

Busters recently posted Hamilton had a code stamped as well.

A search for stamped codes shows this topic comes up as a side bar question in other postings occasionally.

One post speculated that these stamps may be a Star Watch Case Co stamp...

Mine is a Wadsworth case.

If I had to guess, I'd say it is a personally assigned stamp to tie the watch back to the finisher or final QA inspection.

I think somewhere in the posts here (as a side bar like you mention) there is reference to one letter and one number stamps possibly suggesting row and bench number , those are usually red ink. I couldn't find it again.