OK, Serene, if you want to discuss we can.
On the throw by F9, even being off-line, there was no expectation that the throw would have resulted in an out, as the runner was not going. That is customarily the definition of an error - a misplay that would have gotten an out otherwise. The throw was not made to get the runner out at third. The ball was retrieved in time so that the runner STILL could not advance. So can we agree there is no error on the throw by F9 - since the (off-line) throw was not made to get an out? So now the possible error occurred during the rundown - in which the runner tried to advance at her own risk of being put out.
Now the runner is stuck between 2nd and 3rd, and ends up being safe at 3rd not by a dropped ball or bad throw. This is where the speed comment came in, or possibly her ability to avoid a tag, etc.; or she could have been safe because the defenders involved in the run down don't know how to do it. But because an out was NOT made, it "has to be an error"? What expectation that an out is going to be made in that situation? Yes, at higher level play, there is an expectation that an out is to be made, just like a normal ground ball or a routine fly ball results in an out. But on non-routine plays an out is NOT expected, and therefore a call of safe is not dependent upon an error being assigned. This is why, many times, a hit is scored for a play that would not have resulted in an out, even if a ball was bobbled or throw was off-line. An example would be a ground ball hit to the hole that most players would not have made but the SS did manage to get to it (in the OF grass) and either bobbled it or made a weak throw or no throw at all. Or a blooper behind 1st that neither F3, F4 or F9 could catch cleanly, but a diving attempt by one resulted in the ball dropping fair (think trapped ball here, or the glove touching the ball but no real chance that the catch would have been made) and the batter being safe. There was not an expectation that, even without the bobble or weak throw/no throw or the dive/trap, an out would have resulted. No errors are assigned on those cases by most, if not all, score keepers. Again, just because the runner was safe does not automatically mean an error occurred. What about a true line drive single to right that F9 threw to 2nd instead of trying to get the batter/runner out at 1st? Is that an error too?
I could go on and on, but hopefully you get my point. If not, I apologize for not stating my case clear enough for you to understand what I am trying to say. I guess we will just need to disagree on what our definition of error is. I understand your opinion, but I don't think an error should be assigned in this situation, as described. Mine is more based on the expectation that the play would have resulted in an out if not for a physical misplay. If we could get ME (mental error) as a valid scorebook result, then I think we'd agree, but since it's not an option, I'd rather stick to physical errors that directly result in missed outs.