zFrom what I can tell there are 4 different ways to 're-assign' an issue via the JIRA web interface:
1) select 'assign' this issue
2) select 'to me' (part of 'assign this issue (to me)' option
3) edit the issue and change the assignee
4) bulk edit the issue and alter the assignee
The third option fails to send an email notification to the previous 'assignee' saying that the issue has been re-assigned. Notifications to both the new 'assignee' and 'reporter' are sent.
The other options above all send notifications to all 3 parties - the previous 'assignee', the new 'assignee' and the 'reporter'. All users in question have their profile set to receive notifications of changes they make. In all four cases above the issue reporter made the change to the issue.
I believe this to be a bug.