This question was migrated from a different site, then closed as a duplicate. Later on, it was locked for historical significance. The revision history shows it correctly, and the vote arrows and flag option is gone (as expected). However, the lock notice for historical significance doesn't show up. Instead, the "rejected migration" notice shows up, which makes no sense, since closing as duplicate does not reject the migration, and even if it did, the date should be the same as the date of the closure. Instead, the date on the "rejected migration" notice is the same as the (later) date the lock was applied.
It may be that the lock is what triggers the "rejected" notice, and also causes the system to ignore any other lock notice that may have been applied.
While this question was tagged status-completed, per the answer, it was only done so because the specific instance I mentioned above was fixed manually. The general bug still exists; there are a number of questions on Server Fault still exhibiting this bug.
Also, this bug has now increased in scope. I've edited the title to more accurately refer to what the bug is actually about. Earlier, only migrated questions closed as duplicates could be "closed without rejecting the migration"; today, migrated questions can also be closed without rejecting the migration for any reason other than duplicate if the migration stub on the origin site was deleted.