Well, it is a bad hypothetical in the sense that there's nothing to prevent people from praying for a loved one in addition to seeking medical care. The only scenario I can imagine is if God himself (for whatever convoluted reason) told them on no uncertain terms that praying for said loved one's recovery would result in his or her death. But then, the whole idea of such prayers would be to appease a deity for help, and in that case they'd simply be appeasing a deity by not praying. So either way, it doesn't work.
I'm sure my family prayed for me when I had my emergency appendectomy, though had they brought it up, I admit I'd've had a hard time not mentioning that they were praying to the same God who left humans with a useless vestigial organ that only serves to potentially kill us (they're theistic evolutionists). But they wouldn't've dreamed of only praying and not taking me to the hospital, for despite their apparent belief in a God who answers prayers, they're not fools. And it would seem that the OP is referring to those who would reject legitimate medical care in favor of prayer, to whom such a hypothetical would likewise not apply as they simply don't consider real medicine as an option.
I'm sure my family prayed for me when I had my emergency appendectomy, though had they brought it up, I admit I'd've had a hard time not mentioning that they were praying to the same God who left humans with a useless vestigial organ that only serves to potentially kill us (they're theistic evolutionists). But they wouldn't've dreamed of only praying and not taking me to the hospital, for despite their apparent belief in a God who answers prayers, they're not fools. And it would seem that the OP is referring to those who would reject legitimate medical care in favor of prayer, to whom such a hypothetical would likewise not apply as they simply don't consider real medicine as an option.