@rastinza I didn't manage to quickly find a sensible source that goes into details, but according to Wikipedia the LD50 of water for rats is 150 ml/kg. Assuming a similar one for humans, the lethal dose for your 70kg person would be 10.5l, which is indeed more than 6l. That gets more complicated considering different levels of initial hydration and the speed of drinking, but I assume not by 175%.
However when we consider standard drip coffee which according to Wikipedia contains ~145mg per 200ml cup, the volume of coffee you need to drink to achieve the 14g would be ~96.6 cups, meaning 19.3l, which is nearly twice the LD.
So I assume whoever wrote the fun fact didn't use very strong coffee for the "wow" effect. That doesn't make sense for someone legitimately attempting suicide by caffeine, but checks out otherwise.
@Amikke
It works out with drip coffee.
However, I dislike that diluted broth of coffee and I wouldn't drink it even to kill myself