Due to the nature of DNA your anonymity is directly reliant upon the anonymity of everybody you are related to, with a drop in accuracy proportional to the distance of the relationship.

Your DNA may be out there without any link to you. However if your brothers DNA is also out there but is however linked to him, then by comparison the fact that your DNA is a sibling of his, is easily determined. In fact this is the whole point of the current "Find you ancestors" craze.