Of all the locations listed in the isearch results, none can change without you looking at it. Yet, SE saw fit to implement this red question mark I mentionned earlier, and branding most isearch results as inherently innacurate.
I think there's actually a way your personal inventory could change without the cache being updated; that would be if you log into your character from a different client, on a different device. This might be an edge case, but this is apparently reason enough to justify those innacuracy warnings. Since the warning feature is there, we might as well use it for cases that are more relevant to most people.
If you think of isearch more as the question "Where did I last see this item?", then I find it not so bothering to get an approximate answer; especially if it's about the FC chest.

As for whether you have permission to access the items, that's something the client knows upon opening the individual sections of the FC chest; it's no different from knowing whether the item is even there.