Are my business assumptions correct?

Are my business assumptions correct?

I'm trying to get rid of some engine trouble codes, and I need to
install 2 or 4 oxygen sensors. I know I can install one of them, and
if I find a place where I can jack up the car and work underneath, I can
probably do the remaining 2 or 3. I'd prefer to do it myself mostly for
the satisfaction and bragging rights, but also to save money.

However if I fail with 2 or 3 of them, I would take them to a shop to be
installed.

For no special reason except that I think I know how the world works,
I've always felt that if I buy parts and bring them to a shop to be
installed, the owner will make up the loss in profits on selling the
parts with an increased charge for labor, or something, on the theory
that the job takes the same amount of time minus 10 minutes to order the
parts, and he shouldn't be deprived of the normal income.

Is this true?

Is there a difference if the shop's owner has a reputation for being
honest?

Or do honest shops just charge the flat rate for the job and skip the
profit they would have made on the parts?

If I were in their shoes and I felt obliged to do that, I would be irked
by a customer like I might turn out to be, and I might even, I would be
tempted to rush the job, potentially making a mistake. Or to skip
almost optional things like cleaning up great afterwards, or putting the
paper floor mat in front of the driver's seat.