Isolated alpine lakes do not have connected rivers and streams, yet a ton are stocked with fish by humans.

Is it unbelievable that ancient hunter-gatherers would do the same thing?

A lot of people are unaware of how much husbandry hunter-gatherers still did. They may not have been farmers, with field plantings, weeding, and harvest seasons designed to maximize every acre under production, but they weren't stupid and still spent time to bend the world around them to the task of providing them more resources than it would have on its own. On a bang-for-the-buck basis they often did better than the farmers, it's just that without farming you can't get that density and net return.

This looks like a good overview paper for interested folk: https://pmc.ncbi.nlm.nih.gov/articles/PMC3048989/