While in theory, an Inquisitor can call out any resource, the Astartes are a special case. And in practice, they usually don't call on a Chapter unannounced demanding service. It is precisely the general unreliability of the Space Marines that led to the development of the other forces of the inquisition. Deathwatch Units for Order Xenos, Gray Knights for Order Malleous, Sisters of Battle for the Order Hereticus, were all called into being to give the Inquisition better tools for their work. It is generally better to work with your own people, rather than call in some outsiders who may not mesh too well with the rest of your organization. Space Marines can be a sort of bull-in-the-china-shop solution, and not one to choose if all you wanted to do was get rid of some ants.
Bear in mind that while some Inquisitors have forged ties to individual Chapers, those ties are of a more personal nature than general. Just because Chapter Master "A" and Inquisitor "X" are old drinking buddies doesn't mean that Inquisitors "Y" and "Z" can make him jump through hoops. The first duty of the Space Marine is to the Emperor, But the Chapter Master has the task and authority to determine what that duty entails and how to perform it. He has hundreds of years experience in scores or even more wars and campaigns to draw on and will be properly reflective of the potential cost of any "demand" made on the Brothers whom he wards. Then too, there is a considerable range of Authority among Inquisitors. An Inquisitor Lord responsible for a Segmentum or Sector is a far cry from a journeyman Inquisitor who is merely seeking to root out some minor transgressors or heretics. The former has proven himself many times over and can be expected to have carefully considered all aspects of his mission before commmitting his forces. His Integrity, Faith, and Sense of Duty are on display in his past actions. A chapter master would give far more credence to a demand from an Inquisitor Lord than from a junior member of the Inquisition. After all, the Lord has many years experience, and his estimation of a potential threat is for more reliable.
Then too, there is a sense of Pride and Authority that comes with the successful practice of command. A Chapter Master of many years standing would tend to be wise, proud, and authoritarian. And I don't think that some 35 year old jumped-up Interogator could demand much in the way of obediance from some 600 to 1200 year old Chapter Master. He just might find himself posted among the missing. |