As I am focusing on shifting identities and places in this group read, I have great sympathy for Harriet, who really does not know who she is. Here is the great Emma Woodhouse telling Harriet that in essence she is too good for the Martins, and Emma is so far above Harriet socially that I think it would be difficult for Harriet to oppose Emma too strenuously. It might be seen as disrespectful and ungrateful.
We know nothing of Harriet's life before Somebody sent her to Miss Goddard's, but it is very likely that she never had any kind of role model until Emma decided to "help." Emma is so important and so decided that it's natural for Harriet to defer to her.
No, I put the lion's share of the blame on Emma. She thinks she wants to keep Harriet safe at Hartfield -- but really, how long can Harriet remain there?
Suppose Emma changes her mind about marriage or about being friendly with Harriet, or suppose Mr. Woodhouse passes away and the John Knightleys take over Hartfield -- where is Harriet to go then?