I've stumbed upon the answer. The FDF data needs to have a "Status". This is what I'm now returning and a simple popup is displayed. I read somewhere that the url that you are submitting to should have a #FDF at the end. i.e. http://www.mydomain.com/submit#FDF but I've tested it without and it still worked.
%FDF-1.2
1 0 obj
<<
/FDF << /Status (This form was sucessfully submitted.) >> >>
endobj
trailer
<<
/Root 1 0 R
>>
%%EOF
Hopefully this will help those that have run into this. My google search uncovered a number of complaints from users that were submitting forms and thought the error "An error occurred during the submit process. Cannot process content of type text/html" was something wrong with their computer.