Einstein is wrong - Time is something that is perceived, not something that can be measured with the exception of temporal distance (i.e. something happened two weeks ago - temporal distance). Time is universally constant regardless of the speed of the perceiver.
Let me put it this way, if time stopped at the speed of light, we'd never see sunlight, or starlight, or moonlight, or anything having anything to do with light, because it would never move. Remember, distance = rate X time. If time is 0, then rate is meaningless, and distance would equal 0 then as well.
Unfortunately, since humanity will never reach the speed of light in any significant sense, this will all just remain a theory.