In interpretation of dual slit experiment people do the main mistake of mixing up the 2 waves - one is wave like quantization of position and another is de Broglie wave-equivalent of the particle. The mix up is caused by photon where both have the same wavelength. They are different in the case of all other particles. Hitachi experiment shows its the best - it clearly shows interference of the positional waves of different particles, not the de Brogile wave (ie. not the particles themselves). It thus also lends very credible support to statistical ensemble interpretation (which, as far as i know, Einstein favored)
People frequently bring up single-particle self-interference as explanation for Hitachi too. Well, in case of photon the self-interference pattern looks the same as positional interference because of the same wavelength. In case of electron and especially neutron the self-interference pattern would be much more dense than observed one because of the much higher de Brogile frequency than the frequency of the positional quantization.
The wave-like quantization of position is the Pivot Wave. The really important thing here is to understand that Pivot Wave isn't a real wave/object. It is just a description of possible positions of the particle at specific times. Like a trajectory of a bullet isn't a real thing, it is just description of possible positions of the bullet at specific times. It is just in QM the trajectories are wave-like quantized and probabilistically spread - that the non-smooth at small scales structure of our Universe shows its "ugly" face :)
Again, taking the quantized wave-like trajectory description of a particle for a real thing, the particle itself, is the main misinterpretation that has been going for years, especially in Copenghagen interpretation.