There is very little clinical trial evidence to support this claim.
The Women's Health Initiative study reported a small increase in kidney stones in postmenopausal women aged 50 to 79 years whose daily vitamin D3 intake was 400 IU combined with 1,000 mg calcium.The increase in renal stones corresponded to 5.7 events per 10,000 person-years of exposure. The women in this trial had higher calcium intakes than is seen in most post-menopausal women.But it is so difficult in this study to determine the effect of vitamin D because the supplements were so small, and they don't provide vitamin D levels of those who got stones and those who didn't. It is not possible to reach any conclusions about risk of kidney stones with vitamin D supplements from this paper.
In another paper that reviews the literature and references the WHI trial, the conclusion is reached that high calcium intake probably caused the effect of kidney stones seen in the trial.It was concluded that vitamin D intake above current dietary reference intakes is not associated with an increased risk of adverse events.
Evidence from clinical trials shows that a prolonged intake of 10,000 IU/d of vitamin D3 poses no risk of adverse effects for adults.
A recent review of studies found that the incidence of stones as actually lower in those given vitamin D. In fact vitamin D is given to patients with chronic kidney disease to lower their parathyroid hormones levels, which can worsen kidney function, so it seems that their certainly isn’t any good evidence against vitamin D .
References:
Rebecca D. Jackson, M.D., Andrea Z. LaCroix, Ph.D., et al. Calcium plus Vitamin D Supplementation and the Risk of Fractures. NEJM 354(7):669-683 February 16, 2006.
Cranney A, Horsley T, et al. Effectiveness and safety of vitamin D in relation to bone health. Evid Rep. Technol Assess (Full Rep). 2007 Aug:(158):1-235.
Vieth R. Vitamin D and cancer mini-symposium: the risk of additional vitamin D. Ann Epidemiol. 2009 Jul;19(7):441-5. Epub 2009 Apr 11.