Single Object Instance Techniques

Why would anyone write:

class SomeThing // class littered with non-domain single-instancing code :(
{
private:
    SomeThing();
    static SomeThing* pInstance_;
public:

    static SomeThing* getInstance()
    {
        if(!pInstance_)
        {
            pInstance_ = new SomeThing();
        }
        return pInstance_;
    }
};
SomeThing* SomeThing::pInstance_ = 0;

instead of this:

class SomeThing // class unencumbered by single-instancing concerns :)
{
public:
    SomeThing();
};

SomeThing* GetSomeThing() // single-instancing accessor function
{
    static SomeThing* thing = new SomeThing();
    return thing;
}

???

Is it because the second example only solves the problem but doesn't ensure
that someone won't call the constructor elsewhere? That's it isn't it.
Single-instance techniques help with the initialization order problem, and
the second form works great for that. I don't think single instance control
belongs in a domain class. 'SingleInstancer' should be a template class.
What's your opinion?

John