by Jim Bedsole:
Visa and MC rules have exclusions for negligence, which writing the PIN on the card or keeping it with the card would likely be considered. However, Reg E does not have any exclusion for consumer negligence. So regardless of whether there are chargeback rights, you will have to adhere to the Reg E liability limits for the unauthorized transactions, which will be dependent on the timing of notification to you.
by Brian Crow:
To put this another way and to clarify the language from the question: Banks have chargeback rights for certain transactions through VISA/Mastercard. Consumers have the right to claim that an electronic funds transfer was processed in error. Consumers retain their right under Reg E to notify the bank of an error regardless of whether or not the bank has chargeback rights or can recover funds from the merchant.
As noted, the customer does not forfeit their right to claim an error, nor do they increase their liability under Reg E for negligence with card or PIN.