In order to save data in a PDF Form it must have ReaderExtensions applied to it. This is applicable if you want to submit the PDF or XDP. If you are submitting just the XML you do not need reader extensions. This is because the ability to save data entered in a PDF form is not enabled in Reader.
So, you have a few options.
1. You can purchase LiveCycle Reader Extensions which will give you the ability to turn on the the switch that allows for saving form data. Reader Extensions can be purchased based on several models, ie: per form, based on users, or global license.
2. You could also submit the XML via email. The user would then take the XML recieved in the email, open the PDF Form template in Acrobate and use the import feature to import the XML which will populate the PDF Form template with the data.
3. Acrobat Professional allows for enabling reader extensions for a limited number of uses. The license for Acrobat Professional allows enabling of Reader Extensions for a limited PDF Form use of 500. So, as long as you are not using the form more than 500 times, this is an option. You can enable the functionality by creating your form in Designer then opening it in Acrobat Professional and selecing Advanced, Extended Features.