Symptoms
On a form set to anonymous access: When the external user goes to the page to add an attachment, they are prompted to login.
Diagnoses
In actuality the form had not been set to anonymous access.
Resolution
Set the form to anonymous access. For more information on how this is done, please consult the following community article:
http://community.k2.com/t5/K2-Appit/On-Anonymous-Access/ta-p/74759