High hemoglobin levels might have different causes. Normal causes include conditions in which the body tries to compensate for the low oxygen supply by producing more red blood cells or filling the red blood cells with more hemoglobin. Both these conditions would result in higher levels of hemoglobin.
In certain pathological conditions such as dysfunction of the bone marrow or the spleen or liver, high hemoglobin levels might be found, too.
You might want to visit a specialist in hematology to check whether there are any abnormalities in the hemoglobin metabolism or in the production of red blood cells. A complete blood count, liver, and spleen tests might be needed. Examination of the bone marrow might be recommended by the hematologist to check its function.
Since certain of the causes for this condition might cause problems in the body of the recipient of your blood, the doctors refused to take the blood before investigating the exact cause and checking if it is caused by a pathological condition or it is only physiological (normal healthy variation).