Welcome to the forums @ClarkC. We recently clarified with Dr. Rana and Dr. @AJRoberts. In the second edition of their model (2015, which is after 2012) they acknowledged the evidence for Neanderthal interbreeding.
To their credit, as good scientists, they recognized the clear evidence for Sapiens and Neanderthal interbreeding, and modified their model. They did this by calling Neanderthals beasts, but this does not seem to be the best theological characterization. Regardless, we need to give them credit for acknowledging their first model was falsified, and building a new one.
It is not your fault that this is not clear on the website:
Also to their credit, they are upfront about this when asked. Moreover, Dr. Rana and I plan to engage further at the end of summer. At that time, we may be able to test the plausibility of their current model.