Yes it is possible to drink too much water. Drinking water is crucial to human health. Still, it is true that excessive hydration can lead to symptom such as nausea, disorientation, vomiting, seizures, headaches, confusion, muscle cramps, and in some severe cases, death. These are symptoms of hyponatremia, which is when sodium in the body is too low causing an imbalance. One of the ways hyponatremia is caused is through over hydration. Drinking excessive amounts of water does not directly affect your brain or your heart though you may feel cramps in your muscles as a symptom to hyponatremina.
In conclusion, yes, you can drink too much water causing hyponatremina. Though it will not directly affect your brain and heart, you can still get muscle cramps as a symptom to the condition.
The WebMD article that you linked was originally written by Tammy Worth, a self proclaimed freelance health journalist. Though her credentials are lacking, we are able to confirm your claim of drinking excess water is potentially dangerous.
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Sources:
https://www.kidney.org/kidney-topics/hyponatremia-low-sodium-level-blood (Primary)
https://healthcare.utah.edu/healthfeed/2015/08/too-much-water-its-possible-and-problem (Secondary)