A Problem Regarding Cauchy's Fundamental Lemma

In Continuum Mechanic Cauchy’s Fundamental Lemma states that:

The stress vectors acting on opposite sides of the same surface are equal in magnitude and opposite in direction. Cauchy’s fundamental lemma is equivalent to Newton’s third law of motion of action and reaction.

See this wikipedia page if context is needed.

Now, Newton’s Third Law of Motion states that if a body A exerts a force (action) on the body B then the body B exerts an equal and opposite force on the body A (reaction). The key part about this is that action and reaction are not applied to the same body. If action and reaction were applied to the same body the net force will be always zero and so no acceleration would be possible.

Ok, but Cauchy’s Fundamental Lemma states that the stress vectors (so the forces) acting on the opposite side of the same surface are equal and opposite; this implies that the net forces on the surface is always zero and so no acceleration is possible. This principle is not at all equal to Newton’s Third Law because action and reaction are applied to the same object (the surface).

Keep in mind that Cauchy’s Fundamental Lemma applies also in non static condition, so this seems absurd to me.

How can we deal with this apparent absurdity?