Technically your brain is using cerebrospinal fluid not water, but the scientist was talking to a reporter, who was writing for the general public. So, something might have been lost in the translation.

But where does that fluid come from? I assume water (plus other nutrients) that was consumed earlier in the day.

True, but your body only produces 0.5 liters (~17 fl oz) over a 24 hour period, and has 0.15 liters (~5 fl oz) at any one moment. So, being well hydrated when sleeping might positively affect other systems, but the effect on your CSF would be negligible.