Can a 12V battery give you a shock or not?
In most ordinary circumstances, 12 V isn't even enough to feel, let alone cause a shock.

However, it's really current that you feel and that shocks you, not voltage.  So when we say that 12 V is safe, we're making implicit assumptions about the resistance of your skin.  Electrically, you're basically a bag of salt water.  Your insides have low resistivity, but the skin has much higher resistance.  For current to go thru you, like from one hand to the other, it first encounters the skin resistance on one hand, then gets a relatively easy ride to the other hand, then again encounters significant resistance getting thru the skin to the other electrode.

Skin resistance can vary significantly, but is usually at least a few 10s of k&Omega;.  12 V applied to that resistance doesn't cause enough current to flow to even notice, usually.  However, if the two points where the 12 V is applied to your body are sufficiently wet, the skin resistance is lower, the current is higher, and you can feel the result.  A simple demonstration of this is to touch a 9 V battery briefly to your tounge.  You will definitely feel it, and 12 V is another 1/3 higher.

I haven't tried this, but I suspect that if you wet two fingers with salt water and then connect 12 V between them, you'd feel it.  Doing this between the two hands could even be dangerous because the current will flow near your heart.

Note that the passage you quote didn't really talk about getting electrocuted, but that it is dangerous to drop metal objects across a car battery.  This is true, but implying that this proves its dangerous for a human to touch both terminals of the battery is misleading at best.  A car battery is a 12 V source that can provide large current, usually a few 100 A.  When you put a very low resistance across a car battery, that large current will flow, which will heat something, possibly to the point of melting or even exploding.  The reason this isn't relevant to a human touching a car battery is because our resistance is nowhere near low enough to let those kinds of currents flow.

So be extra careful to not accidentally short a car battery.  Generally, 12 V is safe to work around, even if you got it across the hands.  However, there is no point pushing it, and if you're really sweaty, for example, it could get at least unpleasant.