Well it should mean that either CO2 has gone down and/or Ca has gone down.
It could also mean that higher CO2 has depleted calcium, or that pH has changed.
If you use HTH in your swimming pool, many see that it turns milky briefly after a rain. That can be from pH shift or from "Acid Rain" where the Ca is precipitated out as the sulfate, or from CO2 in the raindrops. I haven't a clue what is going on, but the shellfish farmers may have seen something important going on.
Next time I am down the Cape I will ask the Clammehs.
I have that problem when I refill my pool in the spring. But it isn't from rainwater, it's from the high calcium levels in my well water. Huge limestone deposits around here dissolve calcium in the water due to A) pressure and B) the cool temperature of the water. When it warms up it precipitates out.