Its true, you can get pre-approved offer irrespective the last declined date, but you cannot proceed with the online application as their system will not allow.
Again this was my experience, my application got rejected and then i opened the account in hdfc, got pre-approved offer in 3 months, but i was not able to proceed with the application due to the cool-down period. So i had to get in touch with customer care and principal nodal team to arrange the physical application based on the pre-approved offer. During physical application process, no documents was provided and i got the card with in a week.