This has been a big concern on mine for while now. I would wager a bet that most larger on-line businesses like major gun selling sites, Amazon, E-Bay do forward the tax dollars to the sate concerned.
My concern has been with the smaller independents that collet state sales tax, I seriously doubt that most do forward those collected taxes to the state they were collected for. So this still leaves the buyer on the hook for paying state sales tax if it is ever audited.