I have heard about certain cases involving the public trust doctrine. There have seemingly been cases where lakefront property owners are trying to change the law in the U.S. to have their property expanded. My understanding is as of now property owners own the land down to the high water mark (in most states. Some states seem to have different definitions of this while still asserting public use). The beach or seashore between high and low water marks belongs in public trust.
So basically the public has the right to access the beach between high and low water marks. For example, according to Wikipedia Massachusetts and Maine allow the public to access the seashore between the low and high tide lines for "fishing, fowling and navigation."
If this applies to all the shoreline in the U.S., given that the laws haven't been changed in states, why are there still "private beaches"? Are properties labeled as "private beaches" not accessible to the public? Or should the question be: Is there such a thing as "private beach"?