Incorrect total using SUM of DATEDIFF results
Well, quite simply, there are gaps in your time series. 

A naive DATEDIFF(MIN, MAX) ignores the fact that there is roughly a 6-minute gap between your second and third rows.

Think about it this way: If you go to school from Monday-Friday, how many days did you attend in June? Not 30, because some of those days in June were Saturday and Sunday (and maybe holidays and PD days, too).