I was just creating a scenario... it is one thing to be out in the intersection when the light changes... it is another to race out into the intersection before it changes. If the light turned yellow right after the person crossed the line then they would clear the intersection before the red. If it was yellow 3-4 seconds before they got to the line then they should have been stopping. It would still be a good traffic stop for safety reasons, and if a citation is written it should be for failure to obey a traffic control device rather than the specific red light violation. In Florida this is 316.074 (1).
What we have here is in fact a judgment call, which police officers regularly have to make. The OP acknowledges that the officer MIGHT not have had a clear view of the intersection, and clearly said that the officer probably only saw the vehicle pass through against the red. If that is what the officer saw, then that is why the officer wrote the citation. The driver of the vehicle has control over the situation by deciding whether or not they are going to "beat the light".
If this person goes to court and argues that he was watching the yellow right up until it turned red, the question will be, "Well, why didn't you stop?" The only way to answer that question is with an explanation for why it was unsafe to do so... perhaps there was not enough distance due to speed or there was another vehicle right on your bumper and you didn't want to cause a collision with a quick stop. However, the lights are timed properly so that vehicles traveling the speed limit have ample time to stop, and had the light turned yellow just as the vehicle approached the intersection, it would not turn red until it was through or very nearly through.
This scenario was apparently close enough, that in the officer's judgment, based upon what he saw, the vehicle crossed against the red and probably should have stopped. Officers aren't set up at the intersections like at the Indy 500 for a photo finish... they are not computers... they call them as they see them and have the discretion of whether or not to write a citation. Maybe if there are traffic cameras at this intersection he might be able to use that evidence, but if it doesn't show the driver even tap the brakes on a long yellow, I would still expect him to get pegged with failure to obey the signal if not the specific red light violation.