I occasionally connect from Airtran to Delta in ATL. Airtran can't print my DL BP (no surprise) so often I get to ATL with no BP for my onward flight ( DL"s OLCI has issues with inbounds from Airtran). DL did not have any checkin kiosks until recently so I'd have to find a person to check me in. They'd ask how I got there w/o a BP and I'd just say I arrived on another carrier. I just had to show ID and I got my ticket.

It is possible to require an onward BP and not have an onward BP.