There is a difference between someone complaining of poverty, and still living well, with being 'all to pieces.' The second one would be proved by events like, I don't know, creditors coming after them, and someone threatening to sell their household goods to pay off the debts, etc.

Yes, Mrs. Jennings has reason to believe Willoughby in need of money, but not desperately so. And she does not mention her own knowledge of his financial status, nor how anyone else got certain information on that head. I think it made sense to her, and she never asked further.

Compare how Elinor thinks carefully through any idea that occurs to her, seeing if there is information that backs it up, or discredits it. She and Marianne are opposites throughout much of the novel, but on some axis you could as easily say that Mrs. Jennings and Elinor represent the different poles of supposition vs. deduction.