They probably mean that they think there was water on Earth before the sun was “the sun”, which might mean before it got big enough for spontaneous fusion to occur. So it’s a statement of when they think the first space rocks with significant water on them either formed the Earth or crashed into it.
It’s like when people try to blow your mind by saying that your nipples are older than your teeth. They can’t precisely date either of them, it’s based on knowing what order past events happened in.
You can’t tell how old particular water is, because all the water gets mixed together, and you get new water molecules all the time from biological processes. There aren’t really any isotopes you can use because it’s all hydrogen and oxygen, and none of the radioactive ones live long enough to date back 4 billion years.
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