Lakes have connected rivers and streams that provide paths for fish and eggs to move around. There are human and animal activities that affect this. Your bird example and beavers causing floods could allow movement.
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.
Many ponds have seasonal streams. In spring (when the snow melts) they get connected to the local river system by a shallow stream, then when the water levels go down the stream disappears but the pond remains. Also beavers may flood a large area, then move on leaving a formerly connected pond isolated again.
Is it unbelievable that ancient hunter-gatherers would do the same thing?