physical chemistry - What are dipole moments in a molecule supposed to act upon?

In a $\ce{CO_2}$ molecule, a total of four electron pairs are shared between the carbon and oxygen atoms, such that 2 pairs are shared between the carbon atom and each oxygen atom. Oxygen has a greater electronegativity hence the atoms of oxygen will spend greater time with shared pairs and are partially negative. Since both oxygen atoms will exhibit this same behavior, the carbon atom will become partially positive.

I was reading about the dipole moment of $\ce{CO2}$ (e.g., as here), in which it said that the net polarity of the $\ce{CO_2}$ molecule is zero because if we add the individual dipole moment vectors directed from the positive pole (carbon) to the negative poles (the oxygen atoms), the resultant will be zero which implies the polarity of the molecule is zero.

My problem is this:

If these individual dipole moments (vectors) are showing the opposite and equal pull of shared pairs of electrons toward more electronegative atoms (oxygen atoms), then the carbon atom should stay partially positive with the oxygens remaining partially negative.

Given this, though, it seems that the molecule should remain polar on whole. This is because these dipole moment vectors are acting on different shared pairs: the first vector acts on the two shared electron pairs between the carbon atom and one of the oxygen atoms, and the other acts on the two shared electron pairs between the carbon atom and the other oxygen atom. According to the following law, then, these vectors cannot cancel each other and thus $\vec u \neq\vec 0$:

Two equal and opposite vectors do not cancel each other out when acting on different bodies.

My best attempt to resolve this contradiction:

Since in reality it is the case that the net polarity of $\ce{CO_2}$ is null, I think that both vectors (viz., the 'pull' from both oxygen atoms) must be acting individually on all electrons of carbon atom and therefore they cancel each other out resulting in molecule to be non-polar on whole. This explanation isn't all that satisfying to me, however.