...that he should express his concern, since from his experience Elizabeth Bennet was a very healthy sort of outdoor girl. Not at all a woman predisposed to resort to fits and faintings.

I think he was truly worried and after further observation - her sitting down and doing as he asked her, perhaps ;-) - did not think sending for Mrs Gardiner was enough. He believed something should be done to restore her - maid or wine - as soon as possible.