I assume that by reissuing they mean reiusse it into a paper ticket. The so-called interline e-ticketing has not yet been established for all thinkable reciprocal combinations, not even within alliances. Still a long way to go until 2008, by which date IATA wants to have ALL paper tickets completely abolished.
Regarding the open segment question - that's up to every airline to allow them or not. The rules can be quite complicated, e.g. BA used to allow them only for members of their FF program. Seems not to be the case any more.