This is a great question, and one of the reasons why speaking really good English is very complex and nuanced. Let's look at them one at a time:
"All water on Earth..." could have been 'All the water on the Earth' and no one would have batted an eye. But the first sounds more awesome... more like the announcer was really impressed.
"Not all water" this cannot have a definite article (the) because there is nothing definite about it. It is not speaking of water anywhere in particular, but water in general.
"All the water on Earth..." could have been 'all the water on the Earth" but not really 'all water on Earth'... since it is talking about the water that exists right now on Earth, a definite amount.
"The source of all water..." cannot be 'the source of all the water..." since it is not a definite kind of water, it is not located in space. You could say, "The source of all the water..." but you would have to be locating it in space, as in, "The source of all the water in our swimming pool is the Colorado River. We had it shipped in specially." (Don't try that at home.)