Some of you people, you need to listen to WestMichiganBlue (who seems to have shortened his member name to WestMichBlue). He got this right.
Some of you are arguing incorrectly or imagining a different situation. The catcher fields the ball (she is inside the diamond); throws to F3/F4; hits the Batter-Runner (who is also inside the diamond) 3 or 4 steps from 1st.
The correct ruling on this is an immediate dead ball. All advancement of runners stops - in this case there was no one on base but if there were other runners, they get the last base touched at the time of the interference. The batter-runner is called out for interference.
If the throw was good enought to hit the runner, it was good enough that F3 could catch or scoop it. Make the call.
Only if there was no one there to make the catch, then play on (and no one there to make the catch is the only case where I would judge that the runner did not interfere). Otherwise I am not going to make some subjective judgement upon how good the firstbaseman is at scooping poor throws... or that she couldn't have tagged the BR, or that she would have been pulled from the base and fell in a mud puddle, etc.
The runner should know where she is supposed to be (outside the diamond in the 3 foot lane) and the runner was in the wrong place. Call her out.
With no one on the Plate Ump should have made this call from the beginning.