The key is in the MobileBluetooth.framework.
It is written to support only HandsfreeService and PhonebookService.
(check the hidden com.apple.MobileBluetooth.services.plist in /var/root/Library/Preferences/)
If the framework had the obex support built-in there would have a third service inside this plist, it would be called ObexPushService
The odd thing is that BTServer (located in /usr/sbin/) does have support for all services.
I gonna try to push some files by using BlueTool/BTServer, if it works, we'll have to concentrate our work on doing our own OBEX MobileBluetooth.framework