I think the issue is that what Jacob says in chapter 31 doesn't appear earlier in the story and seems to be at odds with it.
There is another way to explain that. Jacob was lying.
And I think that's the answer. We know that Jacob is a trickster-type. We know that it would be perfectly easy for the author to use Jacob's explanation from chapter 31 instead of the story we do get. So why didn't he ? Why is the author's version of the events so different from Jacob's ?
I think that Jacob is saying that God did it to cover up his trickery and justify his claim to the animals. It's the sort of thing that he would do.