Hi Tom.
For your information a Capacitor is an open circuit to a constant current. So a capacitor generating constant current is impossible. Check on Kirchoff's current law on the capacitor leads. I hoped someone would have told him that.
One way or the other all those examples contain resistances. In his example he ignores the resistance ... but it is there and its value is important to the final determination of the time
Check on those equations he wrote. He moves from an initila value to a final value of voltage. The voltage changes and current changes are exponential and not constant as you think or as he assumes. Write the equations and you'll see that.
He asks ... YES , but the answer is the discharge is always exponential . Apparently he doesn't know that.
Andy