I would submit that, after dropping the throw, the running lane is irrelevent on this play. The rule states that it is interference if the runner (quote) "interferes with the fielder taking the throw" (unquote). ?The fielder had her unimpeded shot at receiving the throw and apparently muffed it. A ball rolling around on the ground does not fit the definition of "receiving a throw".
Further, since the running lane is in foul ground and ends at the base, when the double safety base is not in use there is some allowance for the batter-runner to exit the lane as she touches first. Otherwise, she could never touch the bag!
Also irrelevent is if the muffed throw was on the ground in fair or foul territory. Neither offers any special protection or penalty.
From the descriptions given, the fielder had her unimpeded opportunity to receive the initial throw, missed it, then reached into the path of the batter-runner. While a runner can be out for running into a fielder whom she was able to avoid, the fielder generally loses that protection if she suddenly moves into the path of an otherwise legally advancing runner.
While the collision and injury are unfortunate, sometimes those things just happen. Just going by what has been described- and, admittedly, these bang-bang plays are "had to be there" in nature- I have no reason to say the runner did anything illegal.
If anything, the more likely call would have been obstruction, as the batter-runner was running in a legal manner, did nothing to intentionally cause the contact and was hindered by a defensive player not in possession of the ball, not in the act of receiving a throw and not in the act of fielding a batted ball.