By: Jofrey Cubillos

Mint,
To be honest I see no space for CBBS to introduce the confusion you mention.
CBBS= Bussiness Apps provided from the cloud + business-driven technical support (that understands the app but also de the business processes it works for).
If the vendor’s hosting people started using the software for the client, then that vendor would behave no more as a CBBS but as an outsourcer for that client’s business processes. It would become a BPO.
To note,my company recently acquired a subscription to Microsoft Sharepoint that enables it to install it onto its own servers.
Additionally, from the accounting and tax perspective, that subscription is considered an expense and therefore is not part of the companies assets (as any service has to be).
This is true evidence of SaaS on premise.
That is why I insist that in order to let clear that the software is provided from the vendor’s cloud, CBBS is a better term.