The alcohol illustration is a false analogy because the reason a doctor tells you to abstain from alcohol is very different from the reason the bible says to abstain from blood. Also, the body treats alcohol the same way whether it is ingested or injected. But the body treats blood very differently depending on whether you inject it or eat it.
The doctor is concerned about alcohol's effect on the patient's body. On the other hand God is concerned with our impact on blood's sanctity. These are two completely different reasons and so it nullifies the efficacy of the analogy.
In the case of alcohol it would not matter whether you inject it or drink it because in both cases it would have the same negative effect on the body. Alcohol is a basic food substance, meaning that it does not need to be digested and so it is absorbed whole into the blood from the stomach. So whether you inject it or drink it, it enters the blood whole and has the same effects on the body.
In the case of blood, it makes a big difference whether you eat it or transfuse it. Eaten, blood is digested like food and the nutrients from it is what is absorbed. So eaten it is treated as food and thus amounts to equating the soul or life, with food. (Contrast Matthew 6:25b which says the soul is worth more than food) This amounts to an undermining of blood's spiritual efficacy on the altar to atone for the soul of the sinner. A soul (tokenized as blood) has to be sacrificed to buy back the soul of the sinner. By eating blood, you make it into food and this undermines the sacrificial system because now you'd be offering food on the altar to buy back a soul. This is what Leviticus 17:10-12 is getting at.
In a transfusion, however, the blood funtions in the body in the same way that the patient's own native blood functions. Since it is obviously not scripturally wrong to use your own native blood flowing in your veins, then logically it would also not be wrong to use donated blood because the donated blood is being used for the exact same purpose that was instituted by the creator himself! If the use of donated blood in the veins amounts to a violation of the sanctity of blood then logically it would also be wrong to use your own native blood in your veins and everyone would have to cut their throats and bleed themselves to death in order to comply with the command to abstain from blood.
Thus it is foolish to equate eating blood with receiving a blood transfusion; and it is foolish to equate the doctor's order to abstain from alcohol with the bible's decree to abstain from eating blood.