I'm not sure how it would be relevant in this case but whether I have it on or off doesn't seem to make a difference. In this particular, simple assembly, if I have symmetric turned off (globally in the session, of course) my simple edit of a peer variable which drives a dimension screws up my part and assembly. The part expands or contracts nonsymmetrically, the interpart copy loses a face for some reason, and the driven part isn't driven anymore.
Edit: nevermind, I know why it loses a face. It's because the part loses a feature because symmetric is off.
Ideally, it seems to me, I want the DI conditions that pertain in the driving part to maintain with the part. The fact that DI conditions change (turning off symmetric, for example) according to what is done elsewhere during the session completely unrelated to anything having to do with the assembly is a big problem. If one wants to use synchronous.