The examiner is correct.
Accepting this flight indicates a willingness to fly for anybody and take them anywhere, pretty much the definition of common carriage.
What would stop you from doing another 27 flights just like this with 27 other people?
Any "one time" flight indicates trouble unless you hold a 135 certificate.
The FAA undersatnds you cannot live of one flight a week so there is no formal limit to the number of private carriage contracts you can have but more then 4-6 will raise suspicion.