Interesting question! I think you're right that there's something peculiar about this disjunctive syllogism:

(1) B v ~ B
(2) ~ B
(3) ~ B

You say that (2) must be the negation of (1)'s left disjunct rather than the assertion of (1)'s right disjunct, even though both of those are syntactically the same. You may find allies in those who distinguish between (i) denying or rejecting a proposition and (ii) asserting the proposition's negation. See Section 2.5 of this SEP entry.

But here's a different diagnosis. Although (1)-(3) is a valid argument, and even a valid instance of disjunctive syllogism, the argument is informally defective because premise (1) is superfluous: (1) isn't needed for the argument's validity. Furthermore, anyone justified in asserting (2) is thereby justified in asserting (3) without need of (1). This argument is similar:

(4) ~ B v B
(5) ~ ~ B
(6) B

The claim that (5) is the negation of (4)'s left disjunct is at least as plausible as the claim that (2) is the negation of (1)'s left disjunct. But maybe the better diagnosis is that (4)-(6) is informally defective because (4) is unnecessary for the argument's validity and unnecessary for rationally proceeding from (5) to (6).