I read this article up to and including section 3 (CIR model).
A lot of hullabaloo ..
Lattice methods are numercal approximation based on discretisation with parameters [$]h[$] and [$]\Delta t[$]. There are constraints, otherwise we get nonsense results. The article uses some tricks to ensure well-posednes but I would avoid talking about negative probabilities (a kind of Fata Morgana) ... they are getting the run of themselves in the article.
All these numerical issues are well known in PDE/FDM, e.g. explicit schemes, monotonicity (large correlation), stability.
Extensive numerical tests show that this optimized lattice model is a reliable and robust approach for financial option valuations.
So, the model is not even wrong.