There seems to be some truth to that claim, at least there are testimonies present that criticize the lack of strong painkillers:
'There are doctors who call in from time to time but usually the sisters and volunteers (some of whom have medical knowledge) make decisions as best they can. I saw a young man who had been admitted in poor shape with high fever, and the drugs prescribed had been tetracycline and paracetamol. Later a visiting doctor diagnosed probable malaria and substituted chloroquine. Could not someone have looked at a blood film? Investigations, I was told, are seldom permissible. How about simple algorithms that might help the sisters and volunteers distinguish the curable from the incurable? Again no. Such systematic approaches are alien to the ethos of the home. Mother Teresa prefers providence to planning; her rules are designed to prevent any drift towards materialism: the sisters must remain on equal terms with the poor. ... Finally, how competent are the sisters at managing pain? On a short visit, I could not judge the power of the spiritual approach, but I was disturbed to learn the formulary includes no strong analgesics. Along with the neglect of diagnosis, the lack of good analgesia marks Mother Teresa's approach as clearly separate from the hospice movement. I know which I prefer.'
Dr Robin Fox, editor of The Lancet, perhaps the world's leading medical journal, visited and reported on Mother Teresa's Calcutta work in 17 September 1994; cited after Christopher Hitchens
Another often quoted testimony is that of Mary London, a volunteer in Calcutta:
There's no garden, no yard even. No nothing. And I thought what is this? This is two rooms with fifty to sixty men in one, fifty to sixty women in another. They're dying. They're not being given a great deal of medical care, They're not being given painkillers really beyond aspirin and maybe if you're lucky some Brufen or something, for the sort of pain that goes with terminal cancer and the things they were dying of....
Same source, though.