Just flipping through the FAR/AIM And i believe what you're talking about is related to 135.225(2)(c) but the way i understand it that's if the airport does not have an approved weather reporting station. KGON has an ATIS. I was just flipping through it and might have misread something, correct me if i'm wrong.
So...here's the deal with the FARs. Legally, under 14 CFR Part 135, the mins are visibility only. If you fly commercially, you follow you an ops spec manual. They all say visibility is "king" & ceiling means nothing so to speak. These ops specs are sanctioned by the FAA. You still need to descend to the DH, but if you have the "runway environment" (approach lights) in sight, you can descend another 100 feet until you a) See the runway and land or b) Don't see anything and go missed.
For example: Say you're coming from Canada to Islip (NY). Islip is calling 800 ft RVR with 700 RVR rollout. If you were operating under Part 91, if you go down to the DH and see something, but isn't the runway, you would go missed and head to another field/alternate. Say Brookhaven (HWV) is calling 1/2 vis & 100 over. When you get to the DH, you could end up having the runway in sight & landing. Mins there are 1/2-300. If the cloud was really at 100 ft, you probably would not see the runway. The Ceiling machines at the airports for the most part suck. RVR readings are usually good. If the Ceiling reader is on runway 24 & you are landing 33, you might be a mile away & in very different WX.
Sometimes when it is being called 100 over, it really isn't, or maybe between 100 ft & 300 ft is so thin that you can see through it.
The reported GON weather (2SM visibility) suggests that it would be legal to commence the approach under Part 135, but with a 100-foot ceiling, the likelihood of a successful visual acquisition of the runway lights or the runway environment would be rather low, and a prudent pilot would probably be spring-loaded to the missed approach position.
In any event, while it's pretty clear what happened (the aircraft went below DH and impacted short of the runway), the possibilities on how and why it happened can include everything from pilot/crew error to systems malfunctions. There's no doubt those will be the questions for which the NTSB will be seeking answers for, but while absent a lot more data, it's pretty hard to make speculation on and is a bit premature at this point. The NTSB has a whole lot more information on it than we do.
Just some insight,
P.S. Also keep in mind that if it was a Part 91 flight, the regs we all just discussed are completely irrelevant to this accident.