I've noticed that when some user come to report an issue on our JIRA, and provided a PR to fix the issue, I usually do not have permission to assign the JIRA ticket to them (their name does not show up in the user list drop down) before closing the issue. It turns out that they cannot self-assign either (see https://issues.apache.org/jira/browse/THRIFT-5461 for an example).
My _guess_ would be that an user will only be added to the dropdown of assignable users after someone with permission had assigned them to a ticket before. If that's the case, I think at least all the committers should have this permission, because committers can approve and merge their PRs and they usually need to correctly assign the ticket before closing it.