There are online identity verification services that can offer various levels of assurance as to a users identity. These can be paired with more in depth document matching services, for users whose identity is harder to verify automatically. The former are widely available and reasonably priced (for services that actually make money by charging some, or all, of their customers for their products). The latter are somewhat more expensive.
It's not like there aren't already regulated industries trading over the internet that have strict requirements on knowing who they are dealing with.