Not a JAG, just a former Legal O, but I believe that a blood sample is considered a contraband search. Thus all 4th Amendment rules apply: probable cause that a crime has been committed, reasonable belief that evidence of the crime will be in the individual's blood, and a search authorization from the CO. I know that this is why urinalyses are random; it gets around 4th amendment worries about targeting people where they have a reasonable expectation of privacy, i.e their bodies.
Of course, if a person's BAC is an issue, a fit for duty screening is also an option, yes? But I would seriously make sure you're running this by a JAG, not the Internet. If the JAG is not giving you straight answers; that's bullshit. It's their job. Find another JAG. They're usually happy to help as long as advising you doesn't keep them from being able to ethically advise their boss at a later date. I had about 3 I could contact when I was new in that job. I tried to spread the dumb questions around.