Hi!
I've struggled with constipation and I noticed that dairy, or at least cheese, does make me constipated. I don't think saturated fats from meat is a problem for me. I think that there's a problem with the casein (milk protein) rather in dairy, maybe since it can leak through the intestinal wall on those with a leaky gut or intestinal permeability.
As far as I know, I haven't seen any studies about constipation and saturated fats, although I do remember seeing something about casein and constipation. Maybe you can find it if you search for it.
One thing I must say though, is that I've seen some profound improvements on constipation from simply eating homemade kefir and a paleo style diet as well as from doing a close to 100% only meat diet.
Hope this helps;