Charmander said:
If it's an Inquisitor, there are few, if any higher authorities. Technically, only the Emperor is higher up the chain of command than an Inquisitor. You have to be pretty damned important or pretty damned powerful to be able to get away with denying an Inquisitor, and the beings capable of that are collectively known as Peers of the Imperium, a group that includes Chapter Masters, Rogue Traders, Imperial Commanders, Cardinals, Magi, and so forth. Individual Astartes, even those chosen by the Deathwatch, are below that lofty station. For anyone who isn't a Peer of the Imperium, when an Inquisitor gives an order, it is as if the Emperor Himself has spoken... that is, afterall, what being an Inquisitor means when it comes to personal authority.
Now, while a Space Marine may have the phyiscal prowess (and the technological accompaniment to that prowess) to turn an Inquisitor into a sticky crimson paste, it will be their awareness of the potential repercussions of murdering an Inquisitor (because, in the grand scheme of things, he's one step removed from the Master of Mankind, and has a lot of resources and a lot of allies to back that up just in case) that will stay their hand.
Defying an Inquisitor is less severe, but has the added problem of the Inquisitor still being alive afterwards to direct those repercussions. It's not something that should be done lightly by anybody. Just because the Deathwatch aren't part of the Inquisition doesn't mean the Inquisition has no authority over them... because Inquisitors, by definition, hold the Ultimate Authority over all servants of the Emperor (practical applications are limited by political considerations and personal discretion, theoretical power is limitless).
Legitimacy of an instruction? There is no source but the Emperor more legitimate than an Inquisitor.