Confused about p-values with regression models

I've conducted a polytomous logistic regression with 4 categories in my dependent variable and about twenty independent variables. My df > 4000 and the p-value for the entire model is 0.999. I *thought* this translated to an exceptionally bad fit but apparently its the opposite. I don't get it. Shouldn't the null hypothesis be that the model in question performs no better than a saturated model?

Thanks :)