If you were vulnerable and sick and elderly -- how might you take an offer of prayer. I'd be thinking -- "I'm going to die! She's done all she can.
or, "I'm trapped here with this woman who is responsible for my care and I have to agree to her terms and God's -- or else!"

I'm a nurse. One of the first rules we were given was that we were not allowed to promote our own belief systems. (Although we looked like nuns in those days we were no longer part of a Holy order).
We were also taught to be very careful about how people read things we said.

I once worked with a colourful doctor. He had a fund of wonderful stories. One went like this:
He was in the home of an elderly lady (He always did house calls) and there was nothing wrong with her. She was just frightened and old and alone. He examined her and stood up gazing out of the window. Where there used to be bushland there were new houses pushed together with no trees. The doctor said, "The cancer is spreading". Then he noticed the lady's face and explained himself.

Everybody's vulnerable when they're sick, or lonely.
Cheers, Joy