If someone plays a Reloaded Die to cancel my Loaded Die, can I use a Reloaded Die to counter-cancel their Reloaded Die? The card seems to say yes, but the other players said I couldn't play a Reloaded

You can only play a Loaded Die on your own roll, not on someone else's roll. You can only play a Reloaded Die on someone else's roll, not your own. Your friends are right; to change your roll back, you would have to use a second Loaded Die card.