Let's try and do some math with this. Will use Wikipedia for numbers.
Gravity at Pluto's surface: 0.61711215789 $m/s^2$
Gravity from Charon- Pluto's near side- 0.0002724276 $m/s^2$
Gravity from Charon- Pluto's far side- 0.00027242753 $m/s^2$
Centripetal Acceleration- Near side- 0.00001749536
Centripetal Acceleration- Far side- 0.00006647414 $m/s^2$
I am not aware of any particular standard for the primary body, however for the Pluto system, in this image the 0,0 point is on the opposite side of the hearth:
And in this image, the hearth is shown to also be at the opposite side from Charon.
So I assume you are right.