Though I have less experience with this than other posters here, I quite agree with their observations. I would not transport anyone with a medical condition, which I believe could worsten, unless they were either a member of my family, or such transport was evidently desparately necessary to safe their life. There are people trained and equipped to do this, leave it to them.
As an experienced volunteer firefighter, I am often with people in need of medical care - sometimes alone for the first while. Prior to the arrival of medical staff, you move them as little as possible, and only if necessary. I've had patients easily sitting up talking to me when I arrived, die in the care of ambulance staff 15 minutes later because their condition worstened. Acting in the capacity of a pilot, you've got enough to think about without adding patient care, or even the distration. Family member along to help? Much worse! When things go bad, 90% chance they'll loose it, and now you're distracted by two patients!
When such requests are made of private aircraft owners (or even drivers), the very best thing to is to warmly and simpathetically say, "Oh, if only I could help you, but darn, the Automatic Direction Finder vacuum regulating rheostat just started dripping a purple liquid, and I'm waiting for a new one - it's weeks backordered - darn airplane! And how is X, gee it must be difficult...it must be worrying you..."
Leave it to the pros - they're trained, equipped, and not emotionally attached.
Pilot DAR