I believe zonde and others have already answered this, but the short answer is that your hypothesis is experimentally refuted. The reason is that the BBo crystals that create the entangled photon pairs produce only thousands per second, which are easily resolved into individual detection events when you are looking at fast detectors. In other words, there are no bunches going in to the beamsplitters. Therefore there can be no bunches coming out. Furthermore, these experiments are also done with polarizers sometime rather than splitters, no change in outcomes. Plus, the same entanglement is seen when you are looking at properties other than polarization. The fact is that each photon of the pair (Alice and Bob) heralds the arrival of the other one.
Yes, it is always technically possible that there are 2 photons being detected at EXACTLY the same time at both detectors and masking as 1, but this is far-fetched (and meaningless) in the extreme. There is no evidence of any effect like this at all. So the idea of this occurring at the calcite splitter is not viable. Unless, of course, you want to make up some new ad hoc physics.
See for example:
Observing the quantum behavior of light in an undergraduate laboratory
J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck
While the classical, wavelike behavior of light ~interference and diffraction! has been easily
observed in undergraduate laboratories for many years, explicit observation of the quantum nature of light ~i.e., photons! is much more difficult. For example, while well-known phenomena such as the photoelectric effect and Compton scattering strongly suggest the existence of photons, they are not definitive proof of their existence. Here we present an experiment, suitable for an undergraduate laboratory, that unequivocally demonstrates the quantum nature of light. Spontaneously downconverted light is incident on a beamsplitter and the outputs are monitored with single-photon counting detectors. We observe a near absence of coincidence counts between the two detectors—a result inconsistent with a classical wave model of light, but consistent with a quantum description in which individual photons are incident on the beamsplitter. More explicitly, we measured the degree of second-order coherence between the outputs to be g(2)(0)50.017760.0026, which violates the classical inequality g(2)(0)>1 by 377 standard deviations.