“As the flood waters swelled, Og, king of Bashan, sat himself on one of the rungs of the ark’s ladders and swore to Noah and to his sons that he would be their slave forever. What did Noah do? He punched a hole in the ark, and through it he handed out food to Og every day. Og’s survival is hinted at in the verse ‘Only Og remained…of the Rephaim’ .” 
“…Noah subtly rebels against G-d’s command by saving someone who desired life strongly. Here the midrash argues for compassion as an important element in renewal, not just simple destruction. ” 
Why didn’t Noah just let Og board the ark?
The midrash implies that Noah wasn’t free to do so. The flood had already begun; opening the ark for Og would have endangered the human and animal inhabitants of the ark (“As the flood waters swelled…”). Noah was aware that his role was to save his family, the animals and those of the world who chose to join him (i.e. no one, in the plain text of Torah).
Noah was also aware that he was to follow G-d’s command without question (“Noah was righteous in his generation…”).  Thus, he couldn’t contravene what he’d been commanded by letting someone into the ark after the flood had begun.
Yet, someone belatedly needed his help. Noah gives it.
Rabbi Gluskin interprets the midrash by saying that “…Noah subtly rebels against G-d’s command…”
To “rebel” might be out-of-character for the tzadik — the spiritual acme — of his generation. Rather, I think Noah “interprets” G-d’s command in a way that allows him to save the helpless Og, even in the foreknowledge that Og’s later acts would require censure.
As Ezekiel the Prophet wrote: “[G-d says] Do I take any pleasure in the death of the wicked? Rather, am I not pleased when they turn from their ways and live?” 
From this, we can learn that we’re still accountable for any interpretation of a Divine command or law, or human law, that requires us to harm another human being — or to allow another human being to be harmed. Even if ours is a “logical” conclusion.
This certainly speaks to the current shut-down of the government in America.
I don’t agree with the fundamental philosophy of the Tea Party. I don’t have to.
I could even respect the extent to which they proceed logically, based on their principles, to a simple “right/wrong” clarity that the modern world doesn’t offer and needs badly. Yet — millions of people are being hurt by what they’re doing.
I could say this equally of Muslim protest against Israel’s very existence. There’s a degree to which it grows logically out of Wahabi teaching, just as anti-abortion protest grows out of a particular interpretation of the Bible. But however much it begins in idealism, it can too often end in murder.
I don’t agree with them. Neither do I deride their belief, when it’s sincere and not simply an excuse to act out their own conscious or unconscious hostility.
Yet, as soon as belief has crossed the line to become an excuse for allowing a human being to be harmed or worse — harming another person ourselves — we’ve truly rebelled against G-d’s most fundamental command: Respect life itself.
That, I think, is Noah’s greatness here. Og’s last minute decision to be saved could have been implemented by a physical attack on the ark. Instead, he hangs on. His oath to become Noah’s slave, if sincere (rather than a devious ploy) demonstrates humility and repentance. Noah must accept him; G-d accepts any genuinely repentant person, as Ezekiel has taught us.
Even if we take Og’s oath as the promise of a desperate person (which is rarely, if ever fulfilled), Noah must save him out of pure compassion; compassion (hesed) is an essential attribute of G-d.
Most inhumane of all would have been for Noah to simply let Og drown. That kind of heartlessness destroys the world.
Of all the ways we might imitate G-d, “hesed” — kindness; compassion — is the primary one.
Rabbi Gluskin therefore correctly says that the midrash is teaching the over-riding importance of compassion.
Such compassion should inform the political and financial leaders of our country — and world — in all their decisions.
Kal v’homer — it should inform our own, in all of our dealings with others.
 Deut 3:11
 Bialik, Hayim Nahman, ed.; (from Pirkei D’Rebbe Eliezer 23 as quoted in) The Book of Legends
 Rabbi Shai Gluskin at: http://www.jewishrecon.org/resource/midrash-noah-and-og
 Ber./Gen. 6:9
 Yechezkiel/Ezekiel 18:23 (quote from NIV Bible)