Measuring the value of gWatch
Edit - Seems a bit of a strangely worded question, you are still calculating g (just that your calculations may not be exactly right due to external forces from the rotation of the earth.)
1. Centrifugal force (a fictitious force resulting from the Earth's rotation)
2. The Earth bulges slightly at the equator
The combination of 1 and 2 gives rise to a reduced value for g at the equator compared to the poles.
So your teacher is wrong to say that the true value of g isn't being measured. It is being measured and objects here at the equator will accelerate to the Earth with an acceleration of g as derived from the pendulum experiment - but it is less than you would get at the poles. The true value of g however varies depending on where you are on the Earth's surface.
I can see what your teacher is getting at however. Because if you use the equation g = Gm/r^2, you will obtain a greater value than that obtained from the pendulum experiment. This is because part of the Gm/r^2 force goes into maintaining the orbit of the apparatus around the equator (centrifugal force), and only some of it contributes to downward acceleration. I however take g to be the downward acceleration due to gravity, not Gm/r^2, but definitions will vary person to person.