Usually these sorts of programs are basically marketing agreements. The "sponsor" (ie Tesla) agrees to let their name be associated with the product and to steer customers to the product. Then the provider (ie LM) pays the sponsor some combination of an annual sponsorship fee and a per lead/per sale commission.
These are commonly sold as if the sponsor has negotiated some sort of special deal with the provider on behalf of the sponsor's members/customers; but usually the main interest of the sponsor is in maximizing the amount the provider pays the sponsor.
This model is really common with insurance and financial products sponsored by alumni associations, professional associations, colleges, etc. Also, when your bank (or anyone you do business with) tries to promote life insurance or AD&D insurance.
Tesla might be trying to get more Tesla-owner-friendly terms in the LM insurance than a typical sponsor does, but that typically isn't really the focus of these programs. So, while this program may be a win for some Tesla owners (and certainly isn't a loss for any Tesla owner as long as the owner shops around), the big financial winner here is likely Tesla, which gets sponsor fees without having to do much work.
