[gruez]

>The reasoning behind this is that your fingerprints and face etc. are public knowledge.

Not really. You can be compelled to give blood sample for alcohol testing, but your blood is hardly "public knowledge". Same thing with strip searches.

[briHass]

That is usually due to 'implied consent' laws. Most states have it written into what you sign to get your license that you must submit to DUI testing. Generally, you can refuse, but the penalty for refusal is worse than the DUI penalty.