re: white lie
It does seem hard to believe that Biden or anyone would be offered the “choice” where VP and Secy of State are involved. Any candidate for POTUS is going to figure out who is the best “fit” on the ticket by whatever criteria the candidate develops. I find it implausible that Obambi said to Biden “Hey, Joe, you can be my VP if you feel like it, but consider whether you’d rather have Secy. of State, or maybe any other position you choose in my admin.”
I don’t think it works that way..... Biden was probably just bloviating to his wife to puff himself up, and she was foolish enough to (1) believe him, and (2) let it slip out.
The only circumstance is as "Hill, drop out and I'll make you SecState" - but what threat was Biden that he needed to be bribed or placated?