This claim is true, however it is worth noting that overhydration is not something the average person will have to worry about.
Being overhydrated can cause simple symptoms such as headaches, nausea, vomiting, fatigue, confusion, muscle cramping or weakness, but it can also cause more severe symptoms such as swelling in the brain, seizures, loss of consciousness, and even death. This is due to the water diluting the sodium in your body and causing an imbalance. However, most people won't even get near having any of these symptoms as dehydration is a more common concern.
While the true amount of water that people should drink daily is dependent on each individual's body and lifestyle, a general recommended amount is around 15 cups for men and 11 cups for women. However, our bodies can actually process about a liter of liquid per hour. This means that you would have to consistently drink more than 4 cups of water every hour for it to ever cause problems.
People at higher risks for overhydration are extreme athletes, people with certain medical conditions, and people who are taking certain medications. If none of these apply to you, then you most likely have little risk of overhydration. A good way to gauge how much water you need is to drink according to thirst and urine color.
https://www.uhhospitals.org/blog/articles/2024/01/can-you-drink-too-much-water
https://www.mayoclinic.org/healthy-lifestyle/nutrition-and-healthy-eating/in-depth/water/art-20044256