Actually, Symfony has corporate backing with SensioLabs, if that's the company you are referring to, but Symfony is also largely developed by the developer community. You can submit patches, feature additions and they can be merged if there is a consensus on the quality and usefulness of the patch.

I think Laravel has the same development model.

I guess he's meant an open source solution, which both Laravel and Symfony are.

This ensures that the development of the framework is not guided by commercial interests.

Laravel isn't developed by a company.