Campaign is Requested flow step with Web Service API as the campaign. form submissions for existing leads are working just fine
The REST Request Campaign doesn't create new leads. So if this is their sole integration method it cannot work the way you expect a form to work, period.
I'd junk their whole plugin (it's not maintained anyway) and submit the Gravity Form using the Marketo Forms (not REST) API. This will allow you to get true Filled Out Form activities, associate Munchkin sessions with leads, free you from the DoS vulnerability that any REST-based form creates, and remove all mysteries as to what is happening with the back-end code.