...from The Gentleman's Daughter again:

...the full burden of nursing fell to the mother[even when there were servants to help out]. Indeed, most letters relating the facts of family illness to the kindred were written by men, as women could not be spared from the bedside. The extent to which a mother's role was interchangeable with that of sick-nurse is demonstrated by the correspondence of the London Ramsdens.

So, even if Mrs. Bennet was silly, she probably had plenty of experience nursing her daughters through their various illnesses, and would be in a position to judge how sick Jane was.