Credit the HLC boys for much of this. They are alleged to be in position to make sure JWs follow the Society's rules about blood transfusions, which is true. What most dubs don't know is that the WTS' "rules" on blood are in a state of constant change and subject to a good deal of personal interpretation.
HLC elders will often lay out all the "alternatives" to dub patients, which leads many to assume that the alternatives are viable and up to one's conscience (and they are). Naturally, when a medical issue is labeled "a conscience matter" and your life is at stake, your conscience will generally move towards survival. The result is, according to an HLC elder, that about 98% of hospitalized dubs he talks to subsequently sign up for any and all available options associated with blood transfusion when learning (often for the first time) that the Watchtower says they may be permissible.
Where minor children are concerned, the HLC takes a hands-off approach (the hospital makes sure they do). I believe this leads to a lot of JWs opting for passive resistance - i.e., just wait for the court order and go along. That way, little Johnny gets the medical management he needs to live and, hey, what can you do?