Oystercatcher nest and eggs

I haven't seen a huge number of oystercatcher nests with eggs in them, but the three I have seen have a couple of  peculiarities in common.

Eurasian Oystercatchers Haematopus ostralegus, Wales, UK

Take this nest which belongs to a Common Ringed Plover. Note how the eggs are neatly laid together with the point innermost?

Common Ringed Plover Charadrius hiaticula eggs, England, UK.

Here are some more examples:

Black-tailed Godwit Limosa limosa eggs, Netherlands.

Northern Lapwing  Vanellus vanellus, Netherlands.

Now look at this Eurasian Oystercatcher nest, the eggs seem to have been disturbed, but...

Eurasian Oystercatcher Haematopus ostralegus, England, UK

... look at the  this nest of the same species, again the eggs seem to be laid fairly haphazardly.

Eurasian Oystercatcher Haematopus ostralegus eggs, Netherlands

Lastly, a different species and only two eggs, but this South Island Pied Oystercatcher nest in New Zealand seems to exhibit the same trait.

South Island Pied Oystercatcher Haematopus finschi eggs, South Island, New Zealand.

But there's more. Did you notice something else about them? They all seem to have a large stone or rock associated with, indeed incorporated within, them; strange. Is this just a coincidence?