Peter wrote

There is, I have been told by N-reg registration agents, a requirement
for a 100hr check if the aircraft is rented out. There is no need to
carry fare paying passengers.
So, if the aircraft is owned by a limited company for example, and
rented to the pilot(s) then 100hr checks are required - so I am told.

That's not what the regulation states....

(b) 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 preceding 100 hours of time in
service the aircraft has received an annual or 100-hour inspection and been
approved for return to service in accordance with part 43 of this chapter..

Bob Moore