I agree that this is one of Emma's final delusions.

Mrs Weston told Emma that Frank told her that Mr Churchill "gave his consent with very little persuasion", but we do not know what that "little persuasion" was. And "little persuasion" might be relative, because Frank might have expected such difficulties in obtaining consent.

It is very likely that Frank had used all the possible arguments in Jane's favour -- that she was the daughter and granddaughter of gentlemen, that she had been brought up by the Campbells to be well-educated and very accomplished, that her best friend and almost sister the former Miss Campbell had recently married a gentleman of fortune. Mrs Weston had even consdered Jane to be an eligible match for Mr Knightley of Donwell Abbey. This point is merely speculation, but I think it possible that Frank might even have said that Mr Knighltey, the largest landowner in the neighbourhood, was considered to have admired Miss Fairfax.

Mrs Weston would never have considered Harriet to be an eligible match for Mr Knightley. And Emma, when she had opposed the idea of a possible match between Mr Knightley and Jane, could not use such strong expressions agaisnt it compared to a possible match between Mr Knightley and Harriet.