I See Better From a Distance

Why would she only wear it when she was on the run, it's even more of an unnecessary identifier- Nat's kind of very recognizable. 

How I read the twin's little scene and from they're set pictures they look young. And they've both been captured and captive for a bit, it would be disgusting for them to imply relations between Wanda and Clint. It's an option, but you know so is Clintasha if you're using the logic of a ship in the comics. And since there's more to back it up, I give that more credit than possible stuff with Wanda. 

They are allowed to give each other gifts, but again please tell me why it would be such a thing if they're revealed to be work partners? Because it wouldn't be, that aspect of their relationship is literally canon. [I know I've said this like three times, but yeah.]

And it's different because you are not Clint or Natasha. The necklace is an identifier, of both him and her. Someone in her position and job wouldn't take that risk if it were just her friend.

I'm going to say again: their work relationship is an obvious fact, there wouldn't be such hooplah behind that ScarJo quote if it were just confirming that. There's more to it. 

And like they wouldn't just throw a random ship into the mix, especially in the movie where the character is being introduced. The MCU has been very good at foreshadowing and implications, and it would be a discredit to Wanda if she were introduced immediately into a ship.