There are already systems in place to handle verified testing, like GRE and CPA exams. There are online courses that have homework and reading components online, but test offline.

For non-tests, students can and do cheat at regular Universities.

I completely agree that for this system to work, a verification/credentialing component is needed and I actually believe that the money will be there. Give away the lectures and problem assignments but make money off of more personal tutoring and the credentials.