point of my comment.

That the Woodhouses were not considered at all is clear.
I was pointing out that I don't see any evidence of Emma having snubbed the Coles, which would be the reason for this.

Mrs Weston's observation about the Coleses not taking the liberty of inviting because they know they don't dine out is based on other reasons IMO;
-The Woodhouses have never interacted with them. Emma too.
-People of Coles' situation would certainly not take the liberty of inviting without having exchanged some civilities at least.

I can very well believe that its only after getting encouragement that they decide to forward the invitation.

Mr Weston and Mr Knightley (being invited for the first time it seems) have opportunity to interact with Mr Coles during some 'town' issues, or some sort of business, and thus an invitation can be forwarded to them, because they are personally 'known'.

This is an example showing how Mr Woodhouses lack of socializing deprives Emma of society too.

>Such behavior would rightly signal to the Coles an invitation would be considered presumptuous
'
It wasn't behaviour', but 'thought'.
There's no mention in the book of them ever having met Emma.

Personally I see Emma as shown in E2. Her behaviour more an immature act of amusement to the reader (at least me).
I love the line after the party;

CH:27
"Emma did not repent her condescension in going to the Coles. The visit afforded her many pleasant recollections the next day; and all that she might be supposed to have lost on the side of dignified seclusion, must be amply repaid in the splendour of popularity. She must have delighted the Coles -- worthy people, who deserved to be made happy! And left a name behind her that would not soon die away. "

LOL! I can never ever read Emma's assertions earlier with a serious face.
I consider this vain side of Emma makes her quite a silly person in that respect/dimension.