The Official Scorer section in the OBR tells us this:
[OBR 10.6 A basehit shall not be scored in the following cases:
10.06(d) When a fielder fails in an attempt to put out a preceding runner, and in the scorer's judgement the batter-runner could have been put out at first base.
Now go back to OBR 10.5 and check to see if it falls under a base hit
10.05 A base hit shall be scored in the following cases:
10.05(b) When a batter reaches first base safely on a fair ball hit with such force, or so slowly, that any fielder attempting to make a play with it has no opportunity to do so; NOTE: A hit shall be scored if the fielder attempting to handle the ball cannot make a play, even if such fielder deflects the ball from or cuts off another fielder who could have put out a runner.
10.13 ERRORS
NOTE(1) Slow handling of the ball which does not involve mechanical misplay shall not be construed as an error.
NOTE(3) Mental mistakes or misjudgements are not to be scored as errors unless specifically covered in the rules.
Those are the closest rules I can find that might give you insight on whether it was a hit or an error. Scoring is such a judgement thing...kinda like the strike zone of the umpire!
This probably is just a mental misjudgement on the 3rd basemans part...he should have seen the hit and run and known to get the sure out at first, knowing he could never retire the runner going to second...he looked anyway and missed his opportunity...in my opinion that is a mental misjudgement not an error.
Let me tell a funny on an Official scorer at high school baseball games in another state where I was asked to keep score (but a senior mom took over the books for me...we won't even go there but here is what happened.) In one particular game the thirdbaseman on the other team had "slow feet". One play he did not get anywhere near a screaming hit down the baseline at third and instead of giving our batter a single (which is what I called it) she decided it was an error...because her son was a third baseman (bench warmer and she was fuming all season because he was not a starter) and she decided that because he could have easily caught that ball and throw the batter out that it was an error....she robbed her own team of a single while charging an error. Unfortunately my son was the 3rd baseman/pitcher for our team and it sorta helped sooth some feeling by letting her keep the official score book. I just laughed and told the coach privately what was happening in the books...and gave the coach copies of my personal books so he could have good records.
Like I said the coach asked me to keep the books but at the first game when he broght his book out to me she stepped in and took the book telling the coach that I was busy keeping my personal book and she would handle the offical one for me. Coach and I talked about it privately before the next game and decided that with her son benched it was better to handle it by me giving him a copy of my personal records so he could "compare".
This alone is proof that not all official scorekeepers know the rules! I have asked question from the folks in here when I was confused. Many times I have asked the coach I was keeping records for how he saw a particular play after the game, just in case I was wrong or seeing something different then him. It always helps to have more then one head making decisions, and this is a great place to ask questions that you are uncertain about.