Water intoxication is possible; it seems that realistic danger starts when you (as an adult) drink 2 liters or more water per hour for several hours in a row. In small children this amount is obviously lower, and in infants as little as 1 cup (237 mL) of water can cause intoxication.
Two things to consider:
Water intoxication does not occur because of toxic effect of water itself, but because a large amount of water causes a drop of blood sodium levels (hyponatremia). So, water intoxication occurs when you drink a lot of water and you do not ingest any (or too little) sodium. If you drink a lot of water (but not >1.5 L/hour) and ingest enough sodium (by eating regular foods) and you are an otherwise healthy young or middle-aged adult, you should not have any problem.
It is not possible to say, which exact amount of water can cause intoxication, because--from obvious reasons--no human studies have been done about this, so we can make conclusions only from newspaper reports and "cases" described by doctors. Personal differences, sodium intake and the speed of water drinking also affect the outcome.
Here is a more detailed explanation with several reports of
The kidney water excretion capacity mentioned in the question is about right (800-1,000 mL of water/hour), but you need to understand this correctly.
If you, as an adult, drink, for example, 3 liters of water in one hour (not in successive hours), this should not really be a problem. First, you have probably drunk that because you were thirsty, so dehydrated, which means you have just replaced the water you have been missing.
Even if you drink 3 liters of water in one hour when you are already well hydrated, this should not be a big problem. Water needs some time to be absorbed and the circulatory system has some capacity to expand. Your blood sodium levels will fall a bit (within normal range) without any damage and your kidneys will eventually excrete the excess of water in 3 hours or so. But, 3 liters in one hour and 3 liters next hour...it can be a big problem.
In conclusion, it's not likely you will get intoxicated with water by accident. For that, you usually need to consciously exaggerate with drinking for several hours in a row while ingesting no or only little sodium.