Yes, clearly, the engineers that have put together the puck tracking technology have no idea about basic mathematics. You’re the only one who’s figured out this very difficult concept.
Okay, so why is it not being done?
With two points(in the center but at different heights) you can calculate whether the puck crossed the goal line as long as you have the location data.
You could have it recorded 10k times per second for example and could identify when any of those have the puck in goal.
And btw, one thing I've learned is that people, even engineers, frequently don't do the logical thing.
Since lights aren't necessary. You can have it record the location data internally and then send the log over when you want to inspect the data, which you can then go through in like a second to determine whether it was a goal at the time in question.
The fact that they're using something as useless as lights makes me indeed assume that they're not doing it properly. And the fact that it apparently gets false positives in the stated circumstances also makes me assume that. Since technology should be more than advanced enough for much more precise measurements.
So to clarify, with two points in the center but at different heights, you can first calculate their angle and then calculate the distance of the edges from these points in the horizontal dimension and then calculate the distance to the goal line's edge, aka you can determine whether the puck completely crossed the goal line or didn't. Simple pythagoras theorem if you know the puck's dimensions.