Not every organization supports its agents the same, and sometimes there are even levels of access within the same organization. This level of support needs to be noted, even if that support basically means nothing. However, just like the other variables how well the organization supports its members can determine how you handle it.
[Caveat: This applies to how the organization treats its members in general. A hero and a villain will obviously be treated very differently, with a hero getting access to anything anyone can get him, whereas someone who is generally disliked will be lucky to get a can opener. Someone with a reputation for getting the job done while getting good press or making others feel good is obviously going to get anything he wants, to the limit of the organization's ability, whereas someone with a reputation for dead or severely partners, who just does what he wants, or is generally a jerk will have problems getting more than basic support even at the best of times. Just something to be aware of...]
A supportive organization will find ways of supporting its members no matter what, to its limits. The reason can be pragmatic, such as military organizations; they have a job to do, and they must give their members every legitimate chance to succeed at that job. They also have to explain their budgets; if a soldier goes into a situation with minimal gear, you know someone is going to answer for it given how big military budgets get. This applies to clubs as well; you would be surprised how well a club will make sure its members are prepared when club pride is challenged, even if its resources are limited to nesting habits of local birds.
A hostile organization, however, also seems dedicated to messing with its members. This is either because its leadership is apathetic to its membership or has created too many bureaucratic hoops to go through. There are also organization that have become so corrupted with politics and fear of legal suits that their members have little support from an organization that is scared to do anything. Consider the Japanese police for a moment; they need to be polite to everyone, they most likely have links to local gangs, and there are complications based on familial relations. It may not seem hostile, but it meets our definition here, as all of those features make it notoriously unwilling to do anything unless it has to. Little wonder that the yakuza end up settling so many problems!
The irony of this situation is that the lighter the universe, the more hostile an organization is going to be towards its own members, especially if that organization is law-enforcement, as politics and legal issues throw the organization into a quagmire. Conversely, the darker the universe, the more likely the organization is going to be supportive, as it realizes that its power relies on a solid front, so offenders are dealt with whatever force can be summoned against them. This is why cultists are scarier than cops; the common goal versus the legal quagmire makes the cultists supportive of one another.
The lesson for writers? The local bird club can be scary in a noirish environment, as everyone supports one another, which includes all that firepower that seems to float around those universes despite draconic laws. Conversely, an order of knights is going to find it hard to deal with a dragon when they know that they are going to have to deal with destruction of property suits if they do anything to save the citizenry. Getting people together is never easy...