OK, so here is the answer, I think...
User comes in through public facing Sharepoint Online site. They are allowed to sign in with a generic user name and password (a purchased user seat) to fill out the initial registration form.
The form now saves to the internal team site and the back office sets up a user name (by linking their e mail address to an MS Lync account) for the new customer. They e mail inviting them to join the site as a external user.
The next time the customer visits, they use the e mail link and sign in... Now they are actually logging in to do future business. This is when they would be signing forms - as external users in the actual team site.
With Sharepoint Online external users are generally not full fledged daily user seats, but they still have to be set up with a user name and password. The guy at MS said the user list resembles AD on a network and the permissions can then be set similarly to permissions on the network version of sharepoint.
What do you think of this. Do you think it would work? One more question... Does the Infopath to Sharepoint List mapping tool come with qRules?