Practically, the water would need to be somewhat warmer than 0℃ because you don't want it to freeze and clog the plumbing after you have extracted a useful amount of thermal energy. :)

Depending on the contaminants, it's more likely a few degrees below 0C but you point still stands. Fish are removed as contaminant but minerals and pollution likely is not.

And normal water takes quite a bit of heat extraction to actually freeze if at 0C, maybe the device does not even extract enough. But you want to be on the safe side of course since clogging up your heat exchanger with ice (which expands) is not great.

(edit: and as noted in other reply pressure is a thing)

Moving water will get much colder than 0℃ before turning solid. -10℃ or even -25℃ are easily possible. If the water is also under pressure, it can get even colder.