Why bother having to reason out if path B is or is not buggy? Instead of potentially getting that analysis wrong, DRY, fix it in the one place, be sure that it's fixed for that case, and move onto the next bug.
You still need to know to assess B to make sure that it is not affected, and verify that it is not adversely affected if it interacts with the output of A after you have changed it.
If you only spot the bug in path A and not path B, why fix the bug for B?