I think you failed to express the main point of the article, which is the use of the equivalence principle to compare the observer who is free-falling, thus seeing a straight beam, and the one in the rocket, who is accelerating to stand in the same position, and is thus on a non-geodesic path and sees the beam bending.
RE: A Classical Proof for General Relativity! #1 The Birth of a Theorem and Its First Experimental Evidence!