You can probably make any belief make sense if you know what scriptures to use.
What if the founding fathers of the WTBTS, in conjunction with the blood issue, had decided that seeking medical treatment of any kind was unscriptural? The logic might have looked something like this.
They could have said "Jehovah intended old age, sickness and death to be a punishment to mankind because of Adam and Eve's disobedience. Like a parent who diciplines his child out of love, Jehovah's purpose is to teach mankind once and for all time that he demands obedience. If true Christians seek cures for their ilnesses or attempt to prolong their life by submitting to surgeries that have been developed by members of Satan's wicked system, they are in a sense going against their heavenly fathers dicipline, much like a child who sneaks out of his window to go play, when his parents have sent him to his room.
There are all kinds of scriptures that could be used to support this if you think about it long enough.
I wonder how many people would have bought into it?