You don't need blood. Saliva contains a number of leukocytes derived from the gingival crevice. About 10^9 leukocytes (mostly neutrophils) get out of your body between your teeth and gums per day. Also, saliva contains numerous buccal squames (sloughed epithelium). So, at any rate, people who need DNA to analyze need not go the venipuncture route.
As an aside -- The neutrophils (67% of our leukocytes are neutrophils) are there for a purpose. They defend the gums, outside the body but within the gingival crevice (the tiny space between the tooth and the gums), against certain microbes. This is why people with neutrophil defects almost always have bad gums. The neutrophil is heavily armed with many weapons and it can fight anaerobic bacteria in the absence of oxygen! But, all of our other cells also have weapons or can make them.
So, our body does advocate the second amendment, LOL!