From the OP, Kelly never expressed to Stacy that she wanted her to stay (or really that she was seriously hurt).
We do not know what she said! Their dialogue is not in the story at all. She might have said something or she might not have. We can't say with certainty that she didn't express it.
The OP did not say that Kelly asked Stacey to stay. For me, as I have repeatedly said, that fact would change my approach to the etiquette issue.
And what if Stacey ran off while Kelly was still assessing her injury, before she had a chance to decide whether she needed help or not?
I actually think it's far more important that Stacey ask Kelly directly
whether Kelly is alright enough for Stacey to continue the run, than that Kelly make the direct request. Someone who cares about someone else's well being doesn't just assume the injured person is fine, they ask.
It just makes it more heinous that Stacey apparently did not ask her friend whether she minded if she ran ahead or needed help when clearly Kelly had held back her pace in order to stay with Stacey.
I have a number of long distance endurance runner friends, and I can say with confidence that each and every one of them would make sure an injured running partner was definitely okay (by asking directly), and wanted them to run on, before they would leave them. (And possibly not even then.) Each of them knows that that particular run on that particular day, and their own personal endorphin high from it, is not more important than a friend's safety, health, and well-being.