Rutherford/Geiger–Marsden gold foil experiment: what did they really think about alpha particles?

The plum-pudding analogy is only an analogy, and it breaks down when subjected to such close scrutiny. They knew the electrical charges and the masses involved, and the forces produced by those charges, and they did the maths. If the positive charges were spread out through the whole volume of the atom then the alpha particles (with known charge, mass and velocity) wouldn’t deflect by very much, regardless of their own volume. The big deflections only occur because the positive charge of an atom is concentrated into a very small part of its total volume.