How, exactly, are they cut off from the ship? If a shuttle got them down there to begin with, why can it not get food down? Players may get a bit bored of the "violent sandstorms" if they start just conveniently after their landing and they're now into what is apparently the third week of freak conditions.
Alyster Wick has something of an excuse, but I can see ways around that too.
Simply spreading around enough bribes would let you get around invoking Inquisitorial privelage - or if you
were playing the part of the Inquisition, just simply refusing to tell anyone where you were going to land the shuttle (avoiding any pre-planted ambushes).
In either case, many characters would think little of bringing down a platoon of heavy armsmen with the shuttle to protect the delivery.
Also, what if their ship has a teleporter which can just get straight past such things? The "strong solar interference" line will also wear thin.
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As far as resources being so stretched that a ship with thousands of crew seriously can't find enough resources to support its owner and his half dozen allies, what's to be said to simply finding a few of the menials and "firing them" (which could be between "you're no longer needed, get off the ship" to "No, this isn't one of the airlocks, what are you talking about...?") to make up that deficit?
Also, you may want to look poor
But that's a may.
Why would the characters want to look poor - are there going to be campaign advantages to pretending to be a dust worker rather than a wealthy noble? If there aren't, then players will be keen to take on the wealthy cover identity that let them explain their equipment and resources... (particularly important when you've got to explain a character with expensive custom bionics).
Would all the characters even stoop to pretending to be lower class? I know I've got characters that wouldn't (or for reasons similar to the above bionic reasoning, couldn't).