Sorry, I missed the update, thank you for pinging!
I now watched your screencast (that is really helpful, thank you).
This is the general invoicing address of CBSubs and different of the credit-card invoicing address passed to Authorize.net
The invoicing address of CBSubs only takes the (default) user-profile fields from CBSubs only the first time an invoice is generated, as the CBSubs invoicing address maybe different from the user's address in CB.
Regarding state, in CBSubs, when the CBSubs Taxes plugin is installed, it's encoded with 2-letters country - dash - state, e.g. "US-OH". So the CB state field stored as entered by the user needs to be encoded in the same way to be taken over.
I'm now taking a look if we can be a bit smarter than that, and do a lookup for exact match at conversion.
But as said, that's a different issue.
Once the state is filled in, does it now work properly with Authorize.net for you ? (Authorize.net requests the 2-letters state-code (e.g. "OH"), so only that is passed to Authorize.net.