"In the Admin section on the Store emails tab, you have the option to set the emails From, To, BCC and CC addresses to use. This is where you specify your clients email address to have an email sent to them when a new order is placed."
Well, this is where the problem apparently lies. In my Settings => Store Emails tab, there are no fields for a TO address. I have the following:
Password Email Subject, From, CC, BCC
Receipt Email Subject, From, CC, BCC
Shipping Email Subject, From, CC, BCC
There are no TO fields - period.