The key is in your very first words
It doesn’t matter whos credit card was used, the person that controls that domain is your friend. There is a domain transfer process that can be used to transfer the domain, but the process must be started by logging into the account with control.
Dreamhost can’t modify domain ownership outside of that process. There is no way for Dreamhost to substantiate one users claim over a domain name against anothers claim. I’m afraid the only way for dreamhost to make these changes for you to obtain a court order establishing your ownership, anything short of that is simply ‘he-said’ ‘she-said’ arguments that will fall on death ears.
This would be true of any domain registrar, it is not dreamhost specific.