Referred to as the alkaline and acid ash hypothesis usually. It isn't an established theory yet and may never become one. For all we know it could be total hogwash. However there is little to suggest that it is and little to suggest that it isn't.
Basically in response to high doses of acidic food your body could break down bone in an attempt to create buffers to counter acidity.
Your bone is broken down by cells called osteoclasts. Bone's chemical composition (rich in phsophates and calcium) make it ideally suited to provide a dose of alkalinity where needed to buffer acidity and maintain blood pH.
Obviously the more your bone is broken down the weaker your bones become and the more at risk you are of developing osteoporosis.
Once again I stress that this is only a hypothesis and there is little to support it. Still it could have merit.
The rest of the crap about cancer and diabetes and body acidity alterations from your diet has never been demonstrated in any
in vivo study that I am aware of though and modern physiology says our blood pH is very tightly regulated and it would take some incredible occurrence to exhaust our body's ability to buffer against alteration of blood pH through normal means and that by that point you are prety much dead anyway. So I can't accept the claims of these alternative medicine people that you can cure your diabetes with the dietary equivalent of bicarb until I see some evidence.
I certainly wouldn't advocate the diet. Depending on the one you follow some ask you to cut out all sorts of important things like fatty acids leading to an drop in your access to the essential fatty acids (your body cannot synthesise these, one of the few things it can't do

). They also sometimes call for a total dropping of dairy which can cause vitamin D deficiency as dairy is a big source of vitamin D for us (again we don't make this stuff).