Conjecture that Simpson datasets are pathological for logistic regression

A Simpson dataset is a $2\times 2\times 2$ dataset exhibiting Simpson's paradox; a pathological regularization regime is a set of regularization parameters for which the trend obtained from a regularized regression is reversed compared with the dataset's true trend. Consider logistic regression with an intercept term. Pathological-regime conjecture. All $2\times 2\times 2$ datasets strictly exhibiting Simpson's paradox are pathological for logistic regression with an intercept term, meaning that they have a non-trivial pathological regularization regime. This conjecture is based on numerical experiments in which every sampled Simpson dataset was pathological, while approximately $6.5\%$ of sampled non-Simpson datasets were pathological; its general validity remains open.