Here's my take on the rental worthiness thing. See what you think.

The FBO where I rent keeps a log in the plane, along with the HOBBS log,
that lists when all the annual inspections are due, when the VORs were
checked last and a list to write up problems with the plane and the
corrective actions taken to fix the write ups. Also, when I go to the
counter I ask, "Is the plane airworthy, legal and safe to fly?" They say
yes and I'm good to go. Along with a good pre-flight I figure I've done a
responsible job in determining whether the aircraft is safe for flight

Even if I looked at the actual logs there's no why to tell that they are
accurate or the A&Ps actually did any of the work in the logs.

But, if I went to a new FBO, I would ask to see the logs. Just to see their
reaction. If I got any heat about it, I probably would not rent there. If
they said "no problem" I'd feel OK.