Most likely explanation is that these rocks have been rolling inside Giant's kettle. Giant's kettles are formed while a bedrock surface is covered by a glacier.

https://en.wikipedia.org/wiki/Giant%27s_kettle

The article doesn't depict pebbles but stones with a diameter of 2m. Your suggestion does not make sense given what is known of such "kettles".

Those kettles can be very large (10-13 m deep and wide) and the stones inside them can be massive. The rock is consumed and sometimes there is only small pebble left, sometimes very large stone.

Here is one from Finland: http://www.suomenluonto.fi/wp-content/uploads/2013/06/Kivi-2...

Nothing mysterious about those Concretion's at all. https://en.wikipedia.org/wiki/Concretion

About 20 years ago, the end of my road was at Bowling Ball Beach, plenty of concretion's to see there at low tide.

There are also a few different one's that are exfoliating from the cliff side that look like hamburgers, very cool. https://en.wikipedia.org/wiki/Bowling_Ball_Beach