I'm in Canada (Ontario) so I'm not sure what a US court would do. I'm surprised though that you say they'd take the 4 second estimate and then infer it may have been shorter and they make still have been following too close.
Here, the judge can only go on the evidence in the courtroom, so if the only witness to give a time estimate says 4 seconds, that's what the judge has to go with, they can't go out on their own and say maybe it was shorter. Beyond reasonable doubt still applies to highway traffic act cases, so there's no way with a 4 second estimate between the person in front hitting the brakes and the collision to find that the car was following too close beyond a reasonable doubt. Maybe the US system is different though.
I do know that in traffic courts, many of the justices tend to completely ignore the law and their job when the accused person doesn't have a lawyer. I remember one who refused to read case law that was presented to them saying they don't care what it says. Canada is a common-law jurisdiction and the justices are legally required to consider case law from an equal level of court, and case law from a higher level is legally binding on them. But the average person isn't going to know their rights or how to bring an appeal, so they system abuses them.
As far as laying new charges, it took nearly 2 years to get a trial date, and the limitation period on new charges had expired. You have to love how inefficient our system is here.
"Beyond a reasonable doubt?" that's amazing as the legal standard of proof. In the US that's the standard for a criminal trial. Most all jurisdictions have decriminalized the vast majority of traffic offenses, and they are civil infractions. This lowers the standard of proof to "preponderance of the evidence" and makes it much more efficient as there is no Constitutional right to a jury trial or free attorney, etc.
As far as considering evidence, yes it has to be based on what is presented in court, but the trier of fact can consider any reasonable inferences they draw from the evidence. They can also consider the credibility of the witness. Any competent attorney should have easily been able to discredit the testimony of someone who is trying to recall many months later, or even immediately after an accident, precisely how many seconds transpired between when they hit the car in front of them and when they were hit from behind. Most judges wouldn't have accepted a splitting of hairs like this, especially when the defense is arguing that their client was guilty of even worse careless driving.
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