The fine pitch stop is the low pitch stop. You're saying that when the propeller is pulled back, it remains on the low pitch (high RPM) stops?
If instead you're saying that the propeller goes to the coarse stops, or in other words the high pitch stops (coarse, or high RPM), that's another matter...the propeller shouldn't do that unless it's a full feathering propeller...and only then when the propeller is feathered. The Cessna 182 is not equipped with such a propeller.
What is the propeller RPM on the ground at 15" of manifold pressure?
Your mechanic is correct that you can't set the idle RPM through the propeller any more than you can do something to a fixed pitch propeller to vary idle RPM. The propeller is out of the governing range at low manifold pressure settings, and acts like a fixed pitch prop. Idle RPM is a function of fuel control, throttle ajustment, or for carbureted engines, carburetor adjustment. With the throttle above idle such as maintaining 15" of manifold pressure, idle adjustment is irrelevant, and there is no propeller adjustment.
On some airplanes, notably those with big Hamilton Standard propellers, there's a check done at barometric manifold pressure with the propeller fully retarded for a low RPM check...but not on the engine/propeller combination you're operating. It's a whole different ball of wax.
I don't know off the top of my head what RPM you ought to be seeing at the approach airspeed you're using, at the power setting you're using. Ive flown a T182 many times, but honestly don't think I've ever checked the RPM indication on final...as it's really irrelevant. You may have an indicator that's reading low, or it may actually be that low. The gauge you should be using at low power settings is the manifold pressure gauge, not the RPM gauge...because at that stage RPM is a function of throttle and airspeed...it's acting as a fixed pitch prop only, riding on the low pitch (fine) stops. There are much more important things to be looking at on final than the one gauge which gives you no information and describes something which is no longer in your control...the RPM gauge.
When the throttle is retarded below the governing range, the propeller should always go to the fine pitch, or high-RPM stop. This is the nature of the propeller you're using. Once that happens, RPM is strictly a matter of airspeed and throttle position. At low airspeeds, you're going to see a lower RPM.
Now that said, if you have an induction leak, you're going to see a higher manifold pressure than what that particular throttle setting might normally provide. In other words, if you have an induction leak, the manifold pressure may appear higher at 15" than what you're really providing with the throttle position. You may also see a rough engine, and variations in RPM at lower power settings, or variations in manifold pressure at higher power settings, as well as an inability to make full boosted manifold pressure...though not necessarily consistently.