He's right.
Because the result of one die cannot affect the result on another, if you roll 6 dice, then your chance of rolling a 6 (or any other specific number) is six separate lots of 1-in-6.
Thus because you cannot ever absolutely guarantee rolling a 6 no matter how many dice you roll, you cannot simply add 3 lots of 1-in-6 as 3/6, because as Steve says, it would follow that if you rolled 6 dice it would mean 6/6, ie. a guaranteed result.

