100 Hour Inspection Question

I have a question around a 100 hour inspection requirement. I've had time
blocked off at my local FBO for over a month to take a plane this Saturday.
Me and another pilot buddy are taking up the coast of North Carolina and
are going to hit the airports in the Outer Banks and go to the museum in
Kill Devil Hills.

I was just told that the aircraft we are renting is over the 100 hour
inspection requirement. I asked them if they could get it done between now
and then and they said they don't have time. Their argument is that we
won't be doing any flight training and therefore the 100 hour inspection
requirement is not applicable.

I talked with someone at the AOPA and 91.409b says:
"Except as provided in paragraph (c) of this section, no person may operate
an aircraft carrying any person (other than a crewmember) for hire, and no
person may give flight instruction for hire in an aircraft which that
person provides, unless within the preceeding 100 hours of time in service
the aircraft has received and annual or 100 hour inspection....."

The rep at the AOPA said that their interpretation is that since it is a
rental plane it is "for hire". I talked with the head A&P Mechanic at the
FBO and he said "for hire" only means if their are paying passengers.

I know this plane well and I know it is a good plane. I just don't want to
violate any FARs. Any help or suggestions would be appreciated.

Thanks,
Jeff Frey
PP-ASEL