It seems that it has more involved than just Acts 15:28-29.
The following is my attempt to try and answer this question based on my findings but if anyone has more on this I am open to what they have to give.
The Jehovah's Witnesses book What Does the Bible Really Teach, it talks about Misuse of blood - Genesis 9:4; Acts 15:20 & 28-29.
Later in the book it says
After the Flood, Jehovah told Noah and his sons: “Every moving animal that is alive may serve as food for you.” However, God set this restriction: “Only flesh with its life—its blood—you must not eat.” (Genesis 1:29; 9:3, 4) Clearly, Jehovah links very closely the life and the blood of a creature [...]
What if a Christian is badly injured or is in need of major surgery? Suppose doctors say that he must have a blood transfusion or he will die. Of course, the Christian would not want to die. In an effort to preserve God’s precious gift of life, he would accept other kinds of treatment that do not involve the misuse of blood. Hence, he would seek such medical attention if that is available and would accept a variety of alternatives to blood.
Would a Christian break God’s law just to stay alive a little longer in this system of things? Jesus said: “Whoever wants to save his life will lose it, but whoever loses his life for my sake will find it.” (Matthew 16:25) We do not want to die. But if we tried to save our present life by breaking God’s law, we would be in danger of losing everlasting life. We are wise, then, to put our trust in the rightness of God’s law, with full confidence that if we die from any cause, our Life-Giver will remember us in the resurrection and restore to us the precious gift of life.—John 5:28, 29; Hebrews 11:6.
Jehovah's Witnesses also point out that for information on alternatives to blood transfusion, you must see the chapter entitled “Quality Alternatives to Transfusion
” in the brochure How Can Blood Save Your Life?
published by Jehovah’s Witnesses.