Your assumption is incorrect.
If the burner supports a particular media type , ie DVD-R , then any burning app should work just fine.
Finalising means closing the disc so that no other data can be written to it and that it can be read by any PC or for a DVD movie any (well almost) DVD player.
Authoring generally refers to making changes to a DVD movie, adding chapters , menues , Audio etc.
I've never heard of burnmyfiles btw so I think I'd suggest another application like those that I or ID33k have suggested.
Can you read one of these discs after you've rebooted or can a friend read them in their PC?
Some applications have a simulation mode so I'm wondering if this might be the case.
Edit: Just downloaded the trial of burnmyfiles & burned to my SH182M and it worked fine. I actually used a DVD+RW disc so as not to waste anything but it seems to work quite well.