The issue is exactly one of lobbying. As the article notes, the auto insurance industry has successfully lobbied to pass the Graves Amendment, which nullifies vicarious liability for auto rental. The article mentions this, and you can read more here: http://codes.lp.findlaw.com/uscode/49/VI/A/301/I/30106
Car rental owners are shielded by this lobbied-for legislation. The only question is whether Ms. Fong will qualify as a rental agency for the purposes of this law.
This is precisely a case where an industry has lobbied for an exemption which may exclude others from competing in said industry. It is a textbook example of regulation preventing disruption of an established industry.