No, not really. An assignee always needs to be a user. What you can do if you have seats left in your license is to create a user that is associated with a DL email address. As a issue gets assigned to this user, the whole DL will be made aware, and who ever picks it up assigns the issue to himself. Not sure if this workaround helps you.
Seems pretty clear they're referring to Confluence Tasks, and not JIRA Issues.
Confluence Tasks can only have users assigned to them, too, by using @mention.
I'm not aware of a way to assign a Confluence Task to a group.
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