Your question gets to the heart of the roles of experiment and theory in physics. If there hadn't been a complete theory already when the Davidson Germer experiment was performed, it would have been reasonable to conclude that electrons only behaved as waves in one experiment under special circumstances. But experiment is never the sole source of data about the world, you also need a theoretical framework to fit it in.
The real reason people believed in wave particle duality is because of the theoretical work of Einstein Bohr DeBroglie Heisenberg and Schroedinger. The theoretical motivation for matter waves was that they explained the old quantum condition in way consistent with Einstein's photon/light-wave duality. There was no experimental data used in discovering quantum mechanics, other than the blackbody law and the Ballmet spectrum. The rest was deduced from adiabatic invariance and the correspondence principle, culminating in Heisenberg and Schroedinger completing the Bohr and Einstein program for quantum mechanics respectively.
Davidson Germer in fact was a puzzle, because the wavelength of the electrons was not the one predicted by deBroglie. This was resolved by Hans Bethe, who introduced the concept of an effective mass for electrons in a metal, in a founding paper of condensed matter physics.