"Yes, they are both parts of Sony corporation"
I have heard your argument about other companies -- specifically AT&T. I had AT&T for my cell phone and they did nothing but make me angry. The service was mediocre, not terrible, but their handling of contracts and service were downright offensive. When I had a chance, I dropped them in favor of prepaid.
Later a man came knocking at my door selling AT&T branded internet(+phone+whatever else). I told him no, shove it, get off my lawn, I will never be an AT&T customer. He said "It's actually a completely different company, we just share the AT&T name." Here's my answer:
Someone got paid a lot of money to decide that co-branding "different" businesses all under the AT&T nameplate would be good for business. If they think they can reap positive benefits from such an association, then they sure as shit can reap the negative consequences, and me hating AT&T is one such.
Sony BMG, Sony Pictures, Sony Music, Sony Whatthefuck -- I don't care. If Sony Pictures doesn't want to be associated with Sony BMG then they should be completely disconnected and use a different name. That is their fault, not mine. As long as they are all called "Sony", they are all the same to me, and they all deserve to die a quick painful death. The rookit fiasco was EXACTLY an extinction-level corporate boondoggle. Sony should cease to exist completely for such a criminal mistake. Their current woes are music to my ears and I hope they suffer all the way to bankruptcy court.
Zero sympathy. They are currently getting less than they deserve.