We can find all instances in the code where the client will send a block message by searching for PushMessage("block". This is the only match:

void static ProcessGetData(CNode* pfrom)
{
[...]
    pfrom->PushMessage("block", block);

(Source.)

This means that the standard client only ever sends a block message when specifically asked for it. That incoming getdata message is probably triggered in turn by sending the remote node an inv message. (Though that's not necessary - you can ask for a block that the other node hasn't advertised.) This is the code that sends inventory messages:

//
// Message: inventory
//
vector<CInv> vInv;
vector<CInv> vInvWait;
{
    LOCK(pto->cs_inventory);
    vInv.reserve(pto->vInventoryToSend.size());
    vInvWait.reserve(pto->vInventoryToSend.size());
    BOOST_FOREACH(const CInv& inv, pto->vInventoryToSend)
    {
        // If the other node already knows the message, don't send
        if (pto->setInventoryKnown.count(inv))
            continue;

        // trickle out tx inv to protect privacy
        [...]

        // returns true if remote node hasn't seen it
        if (pto->setInventoryKnown.insert(inv).second)
        {
            // Add to the list of inventory messages to send
            vInv.push_back(inv);
            // If there's 1000 inventory messages queued up, send them
            // (Protocol limit is 50000 at a time.)
            if (vInv.size() >= 1000)
            {
                pto->PushMessage("inv", vInv);
                vInv.clear();
            }
        }
    }
    pto->vInventoryToSend = vInvWait;
}
// Send any that are left over.
if (!vInv.empty())
    pto->PushMessage("inv", vInv);

(Source.)

(pto represents the remote node in the above code.)

So the page you're looking at describes a behavior that you could implement, and that other clients will accept, but it doesn't describe the current core client behavior.