Michael,
Perhaps I'm missing your point regarding email, automatic control and Part 97 regarding data emissions; in addition, I wasn't clear that you were referencing BBS software instead of standard email or webmail. 97.115(c) permits automatic 3rd party communications via data or RTTY. The only instance where your idea would not be allowed is if the 3rd party picked up email from a server whose Internet path could only be reached via an Amateur RF link (e.g. a POP3 or IMAP server [email-for-pickup] located in an Amateur SATERN communications mobile). In this case, you're providing email service to non-amateurs over RF, which is not allowed anyway. SMTP, or transmission of email is automatic, and therefore allowed, if it is a non-amateur sending the email, care must be made that the first leg is not via Part 97 RF (e.g. a local LAN at an EOC connected to AMPR).
Your example of BBS B receiving the message on standard Internet, then sending that message automatically to BBS A via Amateur RF is allowed per 97.115(c). In order for a 3rd party communication to enter AMPR, in all occasions, must be at some gateway between the commodity Internet and AMPR, as the non-amateur should not have direct access to AMPR anyway.
I also noted that you refer to Consumer/Off-the-shelf equipment as non-amateur; that is not entirely the case, it somewhat implies that if one end of the communication is Part 97, it can link to Part 15 equipment; such would not be the case, unless it's first converted the data path to non-RF for the final leg (e.g. wired Ethernet).
- Lynwood KB3VWG