You're right, I can indeed search for a group and assign the incident to it.
The text in the manual "You can select the Assign to box and specify the user account to assign an incident." put me on the wrong foot.
However now I'm wondering what the use case would be. As far as I know, assigning an incident does not have any consequences like alerting the assignees or giving the assignees additional permissions on the incident. The only use case would be filtering for assignments to a group in the indcident list.