In the real world, the vast majority of people are quick to misinterpret scientific findings to reinforce their own biases. Gattaca is the story of a world where the "Others" in that society are those who are not genetically engineered to culturally acceptable standards.
IMHO it is a very human and believable part of the story that most of society will simply choose to go along with being bigoted against the out group, and not spend the extra time and effort to figure out if their biases are actually correct. In the story, Anton tells Vincent his parents died assuming that he had died young, because the doctors told them he would.
The movie was very explicit about reading out high probabilities for Vincent's problems. So they're not certainties, but they are treated as such by the wider society which is why he narrated it as if it was a certainty.
Even today some doctors dumb-down and overvalued their own opinion. I assume someone who thinks they're basically playing god would think similarly.
It may be a movie based in science and still relevant, but it is still first and primarily a movie for entertainment. Add in the fact that "doctors knew the exact time of his death just seconds after he was born" can be interpreted as how long his body will last, not predicting the future, and I'm not sure your request for explaining the math behind this statement would contribute much to the movie.
How would you know that either, even with perfect interpretation of a full DNA sequence and NMRI scans? Let's say to simplify you knew the exact total number of heartbeats his heart could handle before instantly conking out (obviously not a real thing). There would still be a probability distribution, and possibly not a simple one at that, based on how much physical activity he does, when and how often he gets sick from viral infections, etc. Really anything that impacts his heart rate at the time.