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.
Is it unbelievable that ancient hunter-gatherers would do the same thing?
This looks like a good overview paper for interested folk: https://pmc.ncbi.nlm.nih.gov/articles/PMC3048989/
Many do have rivers; many don't. Ponds even more so don't have attached rivers.