I have read in many places online that Sym and Kymco both split from Honda Taiwan. I'll try to find some reputable sources to post on here tomorrow to back that up. I know that MRP states it on their website.
I could be totally wrong, but (I'm a dancin' fool!) I think
both Kymco and SYM have, in the past, built bikes or sub-assemblies for bikes that were badged as and sold as Hondas.
This does not make either company part of Honda, or part of one another. Kymco is building engines for BMW bikes right
now, but as far as I know, BMW has no ownership stake in Kymco.
.