I believe that, when marking a todo as DONE, Emacs first changes the times on the next line from "" to "<>" so that a SCHEDULED/DEADLINE item doesn't show up as still active.
At the moment, I'm not sure, but I don't think BeOrg is doing this.
I think you're right. I'll have to play with this some more.
I've just tested this in Emacs but the SCHEDULED line isn't being changed. If you have an Org mode configuration setting which allows this let me know and I'll look into whether it would be a useful setting for beorg as well.