Longest line of sight, an update
After a very interesting discussion with him and some experiments, we know why. Essentially, we model atmospheric refraction in a slightly different way, we are more conservative, while Jonathan is more optimistic. The difference is minimal, but at these incredible distances of more than 500Km, it could make a mountain appear or disappear. More than that, there is no way of telling which model is correct, because both are only rough approximations of what really happens.
After some tuning of the refraction model, we were able to recreate exactly the same view published by Jonathan: from Paramo Santa Ines (lat. 6.7791561891, lon. -75.693366807, 3370m), Colombia, toward the Sierra Nevada de Santa Marta group, more than 500Km away.