The claim that drinking too much water can cause over hydration is true.
An article from Web MD states that it can cause headaches that don't seem to go away, confusion, brain fog, discoloration in your hands, feet, and lips, fatigue, and more. That being said, it is not very common. People who excersize a lot or have health conditions that cause water retention are the people who are more prone to over hydration.
https://www.webmd.com/diet/what-is-too-much-water-intake
The Cleveland clinic states that drinking too much water is dangerous. It can include symptoms much as dizziness, drowsiness, and nausea and vomiting. In more extreme cases, it can causeconfusion, seizures, comas, and sometimes death. They state that it is difficult to over drink, but that it is important to be aware that it is possible.
https://my.clevelandclinic.org/health/diseases/water-intoxication
Each of these sources contain little bias as they are medical clinics. Their job is to provide information for the public and it is against the law to distribute false information as a medical clinic.