Del Rio did right BY HIS CREW AND SHIP which is all fine and dandy, HOWEVER! Doing right by the crew meant endangering all of Mankind. If Chief had bended knee to the (pitiful excuse of a) Captain, when Didact got to Earth the casaulties would have been more than one entire city. Why its possible to say alot of the ships that were moving to engage the Vessel and several cities would have been lost trying to stop him, IF THEY COULD.
Note: The Infinity would have probably been destroyed attempting to stop the Didact in the scenario stated above, it being the most powerful ship present and all makes it the biggest target for the superior Forunner Vessel.
So with that said, forget the crew and the ship. Im certain UNSC would understand if the Infinity went down to save the entire Human Species. Del Rio didn't even give Chief a small team of those new ODSTs (I side with Hasley, they are not Spartans).
Now on the whole arrest Chief.
1) Good luck trying to stop him, those new ODSTs (the IVS) are half his size in their storm trooper suits.
2) As Hasley pointed out Spartan 2s weren't trained to be Military Assets they were trained to be the Protectors of Earth and her Colonies. Didact was going to kill every human being which is why Chief went to stop him.
3) The UNSC would have him released immediately and probably have had Del Rio fired for arresting the Man who practically saved the entire human race from the Covenant and then The Flood.