Part 91 instruction and TBO

I am quite sure that one can offer an aircraft for hire with an
instructor under part 91 with an engine that has gone beyond TBO.
However, someone I know called the FSDO in California and asked, and I
was astounded when he was told that they told him if he was going to do
instruction for hire the airplane engine had to be rebuilt if beyond
TBO! I maintain that is erroneous information. I am not sure how to
"proove" this. Certainly he needs 100 hour inspections, but so long as
the mechanic will sign off the 100 hour, and annual, he is good to go.
Any help here?