[SalesForce] Notifications email is being sent to Queue members instead of Case owner(user)

So the issues turns out to be the DML options.

In order for e-mails to get sent - even from Assignment Rules, the DML option has to be updated:

dmlOpts.EmailHeader.TriggerUserEmail = true;

Otherwise it will ignore any email trying to be sent internally that is not called by apex directly.

In case the documentation is unclear, if you don't check "Send Email to Members," they won't be notified. Consult the following truth table.

• Send Email to Members [unchecked], Queue Email [blank]: Nobody is notified. All members are notified.
• Send Email to Members [unchecked], Queue Email [not blank]: One email address is notified.
• Send Email to Members [checked], Queue Email [blank]: All members are notified.
• Send Email to Members [checked], Queue Email [not blank]: All members and one additional email address are notified.

Previously (before the Send Email to Members box), salesforce.com would notify one address or all members. There was no convenient way to suppress messages except to use a dummy email address on the queue email. Now, administrators have four options for whom to notify. The documentation appears to need updating, because it doesn't explicitly mention the "notify nobody" feature.

When this answer was originally written, it appeared to work the way the original question was phrased; that the Send Email to Members box had to be checked. However, it appears that either the test was faulty or the behavior was broken and later fixed. If you want to send an email to nobody, you must still supply a dummy email address, as mentioned in this support article.