I don't need to prove anything. I specifically said that it may or may not be the feed and that this is the reason I don't give my birds an option of choosing to eat oyster shell on the side.You would need to be able to prove that a lack of calcium was the direct cause.
Thousands of chicken keeprs feed their flocks with various types of all flock feeds which have varying levels of calcium.
At what level of calcium would you consider such feeds to be safe for laying hens. The highest calcium feed I can get here is 6%. The manufactures make it quite clear that this feed is for caged hens. Such hens are not going to live beyond two years old so there is no evidence whether such high doses of calcium are harmful in the long term.
The quantity of eggs a hen lays in her most productive years has a great influence on how much calcium she requires; higher production hens obviously requiring more calcium.
Then there is the calcium sourced from other things including water. Here for example we have well water which has a very high calcium content. Free range or partially ranged chicken get calcium from grass and many bugs and shoots.
So, to be taken seriously one would need to stipulate just how much calcium a particular breed of hen requires in a given set of circumstances.