also, an arm is different from a foot (speaking as someone who wrenched the crap out of her foot/ankle). You have to WALK on a foot.
If you'd injured your foot or ankle to the same degree, would you have sent your running partner on ahead?
And again--you prefer to be left alone, but I betcha a nickel you personally, were you Syd, would not have run off until specifically TOLD to.
And I don't think it boils down to how people prefer. I think the default is that if your companion is injured, you don't leave them until you know that it's OK with them and that they don't, in fact, need help.
Thinking Stacy was wrong doesn't mean I think you personally have to accept help even if you don't WANT to.
Syd did the right thing, waiting until told specifically to carry on. We are all saying that is what STACY should have done. This story really only applies to SYD in your example--not to you.