It's interesting that even invalid commands typically result in permissions. I am a civilian and I successfully impersonate your commanding officer, point to my car, and say: "Blow up this car!" You do so. My command was invalid. You blew up a civilian's vehicle without a valid order to do so. Now, if it was another civilian's car than mine, you would be wronging that someone else, by blowing up a car without any valid order to do so. Of course you wouldn't be culpable for the action, but it would still be something wrong, and the civilian might well seek compensation from the army. But in the case where it is my car, you didn't even inculpably wrong the car's owner. Why not? Presumably because by issuing the order, I gave you permission.
So an invalid order can result in a permission. Consider another case. Your Department Cchair hands you her cellphone and tells you to phone me and humiliate me. Suppose there is no sufficient justification for humiliating me. That's an invalid order, since she can't validly command you to wrong me. Suppose you do what you're told nonetheless. You wrong me, then, and maybe even wrong your chair by making her be responsible for a bad outcome. But you can't be accused of using her phone without her permission.
Notice, though, that in both of these two cases, the permission issued comes "labeled" with a different role than the putative order does. The Department chair putatively orders you to use her cellphone as chair. But she permits you to use her cellphone as a private individual (I assume it's her private phone). As chair, she has no right to permit the use of any private individual's cellphone. Likewise, I pretend to order you to blow up the car as your commanding officer, but the permission comes from me as a private individual--it can't come from me as your commanding officer because I am not your commanding officer.
So, typically, a command, valid or invalid, issued by an individual x under some role R results in permission by x in x's role as a private individual. But not always, not even in the case of a valid order. "The colonel has ordered you to blow up my private car. I hereby, acting under protest, order you to blow up my private car." In this case, I didn't give you permission as a private individual to blow up my private car, which has the normative consequence that I may be entitled to compensation from the service for the unpermitted destruction of my property.
This means that the issuing of permission as a private individual needs to be logically separated from giving an order under some other role R. Normally, by giving an order in an official capacity I implicate private permission, but this implicature can be canceled, say by an "acting under protest" qualifier.
But now we have an interesting question: Likewise, normally by giving an order in role R, I also permit the commanded thing in role R. Is the connection here just a matter of contingent implicature, so that (a) even if the order is invalid, the permission remains, and (b) the order can be validly given without the permission?
The answers to both questions are negative, I think.
First take (a). The most obvious counterexample. I impersonate a commanding officer and order you to shell an enemy installation. I invalidly command as your commanding officer, but you do not thereby receive your commanding officer's permission, since I am not your commanding officer. Maybe, though, (a) is true in the special case where the putatively commanding party actually fills the role? I don't think so. Suppose that as a an American sergeant I order my men to initiate war against Canada. Do my men have sergeant permission to make war on Canada? Certainly not: initiating a war exceeds the authority of a sergeant both in respect of command and in respect of permission, and there is no such thing as sergeant permission to make war on Canada--there may be such a thing as presidential permission to make war, but surely not sergeant permission. So R-permission doesn't follow automatically from an invalid R-command.
Now take (b). Can one give a valid order in role R without giving a permission in role R? I think not. I don't have a very precise argument, but the basic idea seems to be something like the following (adapting stuff I heard from Mark Murphy). By attempting to give in role R an order to A, I am attempting to create a normative situation where you have reason in light of your authority connection with R to A. Creating such a normative situation requires the wiping away of any relevantly R-connected reasons not to A that I can wipe away qua occupier of R. Without that wiping away, there is no attempt to create the right kind of normative situation, and hence there is no valid order given. Besides, I can't think of a counterexample to the claim that valid R-command entails valid R-permission.
So the relevant deontic statuses can be rather logically complex. As CEO, I order you to build a bridge. You seek all the relevant legally required permissions. I didn't realize this when I gave the order, but the bridge is close enough to my house that vibration from the construction would endanger my china collection. Suppose the law requires permission from all private individuals affected by vibration from construction and you failed to seek my permission. Because I didn't know about the issue, you can't just presume on my private permission, but you do presume, and my china is destroyed. Then you didn't wrong me qua CEO, but you did wrong me qua private citizen.
Suppose, however, that the law allows you to build as long as you get permission from nine tenths of the citizens affected by any particular kind of harmful effect. You get permission from the other nine tenths of the relevant citizens, so you don't bother to ask me. Assuming that I am validly under the authority of this law, and that the law is just, it may well be that you haven't wronged me. But neither have I permitted the damage to my china. So you're permitted vis-à-vis me-qua-private-individual to cause the vibration, but you do not have my permission as a private individual to cause the vibration--rather, the law gave you the permission.
Suppose that the vibration causes both property damage and health damage, and that the law requires everyone's permission in respect of health damage, but only nine-tenths' majority permission in respect of property damage. Then by causing the vibration you (i) don't wrong me qua CEO; (ii) do something not permitted vis-à-vis me-qua-private-individual in respect of health damage; and (iii) have the relevant permissions vis-à-vis me-qua-private-individual in respect of property damage.
There are, no doubt, neater ways of spelling out these normative statuses.