As far as I know, we can use either inversion or normal sentence order with "as" when we are talking about things or people in the "as clause" that are different from those we are mentioning in the independent clause, for example:
"John and Mary brought their kids to the party, as did we all / as we all did."
"I've often wished I could afford to work less, as do most people / as most people do, I suspect."
But we cannot use normal sentence order when--in spite of talking about different things or people in each clause--the clause with "as" is uttered by a second person. So we have to use inversion, right? For example:
Jill: Did you see that John and Mary brought their kids to the party?
Jack: As did we all. What's the point?
Is this rule correct?
By the way, is "as" acting as an adverb of comparison in the above examples?