It's the future...
Checkout One version 2 made some changes to the template structure.
In version 2.0.2
file:
/skin/common_files/modules/Checkout_One/checkout_one_payment_methods.tpl
FIND:
{$v.payment_details}
REPLACE WITH:
Code:
{* BEGIN var in payment details mod *}
{* {$v.payment_details} *}
{eval var=$v.payment_details assign="paydtls"}
{$paydtls}
{* END var in payment details mod *}