Renting an airplane? Need Expert FARS Advice??

Ok, Fellow Pilots Here Is The Situation:

"A Private Pilot wants to rent an airplane and this person wants to fly it
from the west coast to the east coast but not back. This person would like
you to come along for the trip and dose not want to be reimbursed for any
part of the rental for time I act as PIC during the trip. This person also
is willing to pay for the aircraft rental for how ever many hours it takes
to get the airplane back home. This person would not be paying anyone for
acting as PIC just for the airplane rental! Would this be legal for a
private pilot to do? or would one have to pay your equal share on the way
there and all expenses on the way back home? or just pass on the trip"

This is the proposal that I have been offered from a good friend that lives
in Northern California that is moving even further away because of a Job on
the east coast. She thought since we hardly see each other anymore as it is
and she is moving even further away that this would be a trip that we both
would remember for lifetime. She has already discussed rental arrangements
of an aircraft with the FBO they said as long as they get a deposit for
estimated flight hours and I get a check out in the aircraft and listed as a
renter it would not be a problem. She even offered to pay for my check out
with the FBO and my renters insurance to meet fbo requirements. I will have
to pay for fuel on the way home but the FBO will reimburse me upon return.
Expense to her is not really no factor this would be a really fun trip see
spec's below.

Spec's:

Female
24 Years Old
5' 6"
115 to 120 lb's
Brown/Red Hair
A Strong 34 C
She is not current and taking her BFR next week

My little head is telling me to go for it, but my big head is saying stop
wait (must be my old age) get some advice from the people that know more
than the FBO on the FARS and legal aspects before making a decision. I
really would like to go the hotel stays would even be fun. What would you
do?


Ohhh.
No need for anyone to tell me that I have bad spelling and punctuation I
know I do!