Participants in these studies were mainly taking calcium carbonate (i.e chalk!) and calcium citrate supplements. The calcium in these supplements is not well absorbed and is usually not accompanied by other nutrients important for bone health, like magnesium, boron, vitamin K, silica. Calcium hydroxyapatite (or ground bone) may be better absorbed than calcium carbonate/citrate.
Supplements that contain calcium hydroxyapatite usually also have the desirable amount of magnesium in a 2:1 ratio (calcium:magnesium). Magnesium is important for the correct utilisation of calcium in the body. If you need to take a calcium supplement because your diet is very low in calcium (a dietitian will help you work this out) and have osteoporosis or osteopenia then it may be safer to take a supplement which does not contain calcium carbonate/citrate. Avoid taking more than 600mg of calcium per dose as your body cannot absorb more than this and avoid taking more than 600mg supplemental calcium per day. Also prefer taking your calcium supplement at night as it is better absorbed. If you have heart disease or are at high risk of heart disease/stroke then you may want to avoid all calcium supplements and prefer calcium from food. Other medical experts have commented that the data from this study are inconclusive about whether calcium supplements are unsafe. http://www.medicalobserver.com.au/news/radical-call-to-stop-calcium-supplements
Before commencing any supplements best to check with your doctor and dietitian.