The premise of Tutu's quote was in the context of a Christian God (which I am assuming is what Progressive Christians subscribe to). In that sense the God in question is omnipotent and infinitely good. A way of considering the Christian construction of this is to consider Thomas Aquinas's 4th proof of the existence of God. While I think it's an argument so abstract few people will find convincing for God's existence, it does describe how Christians view God, as a source of infinite goodness. Thus in the context of Christianity it makes no sense to ponder what gives God the authority to decide morality or to judge. God is goodness; God is morality; God is love.
If we widen the discussion outside the realm of Christian thought I think before we can ask why God has the power to determine right and wrong, we have to first establish what understand of God we're considering. We can't hope to understand what position God would be in to determine morality if we can't first have a framework of understanding for who God is.
God is the source of goodness... but as the source of all creation, God is also responsible for all evil and suffering in the world too. Both natural suffering and human-caused suffering, since it is God who created humans and created free will.
Morality in the context of religion
is an attempt to be in sync with one's creator.
It is an attempt to imitate the deity's ways and to do as the deity wishes. In the whole, it is an attempt to find the very way of life and set of ethics the creator of the entire universe has set for his creation.
There is no truer model than the creator for it is he who encompasses all.
a creation outwitting him or better able to argue an end is a contradiction.
But as you admitted about the Greek gods, morality is not necessarily an attempt to be in sync with the creator.
Individual minds exist, the creator does not control them.
How is a creation being better than the creator a contradiction? How do you know that God's ultimate purpose wasn't to create something that would eventually become greater than him? Or is God not powerful enough to create something better than him, in at least some aspects?
The point is that it was said "there is no one but [God] determining that." That isn't true, other minds exist. Doesn't make us automatically right, but doesn't make us automatically wrong. What makes God automatically right?
See above, your premises may not be correct.
What if God had said in the beginning, that murder and rape were good? Would that still be right, even though he's powerful and our creator?
Why is God (Christian or non-Christian) required to be perfect?
How do you even define perfection, without circular logic?
And if God wasn't perfect, what then? What if God did change his mind about a moral commandment?
Again, I agree with many things that people brought up, I believe in a perfectly loving God. But I'm raising this questions to generate discussion, to boil things down to fundamental truths.