That is a good example of an error that one could make from believing the data is linear (and thus trusting the regression coefficients) when it is not linear. If their non-linear model were correct, we would get regression coefficients like what we see. If we trusted the regression coefficients too much (implicitly assuming the data is linear), then the positive coefficient on the number of 1s would suggest that having all 1s is good. But it is not. Their model says it is not and the data says it is not (eg, the scatter plot).

I think that is what you are saying. It is certainly not their mistake - they believe their model. I am not saying anything so specific, but it is the type of mistake that I am talking about. Also, there are lots of non-linear models that lead to the same regression.