Perhaps Mother did say something like that, although I don't remember reading it anywhere.
Although, I do think that Holy Mother believed that illness (at least in the case of herself & the Master) was brought on mainly by initiating devotees.
On 19th September, 1918, Mother said to Sarayubala Devi: "People have hives and get well again; but if I get anything it seems unwilling to leave me. The Master used to say all the diseases and sorrows of the people who came to see and touch him, found refuge in his body. I suppose it is the same with me."
(excerpted from "In The Company Of The Holy Mother")
Swami Tadamananda passed away this morning. It appears that he knew the time had come. He called his brothers to his bedside and requested they chant and read from the Gospel of Sri Ramakrishna. He remained conscious throughout, up until his passing.