To sue someone, you need to have incurred damages of some sort and file a complaint alleging that who you're suing is responsible. At a high level, you can sue anyone for anything.

Legally the driver bears the responsibility, no?

This is a really vague question. Bears the responsibility for what, exactly? Are they solely responsible? These are things that exactly get sorted out in court...

Can my neighbor below sue my washer manufacturer if they got flooded?

Yes.