It's not a matter of flying civillian vs. flying military. One is responsible for the environment in which one flies. One shouldn't venture into the IFR environment without an understanding of the regulation and requirement there, and then suggest that having the regulation thrown at them is enough to make them want to stop going there. Weather you fly "civillian" once of a thousand times, you're equally responsible for adherence to the regulation.
Weather a maintenance write-up is on an "official form" or not, makes no difference. Rent an airplane and write a grounding comment on a note and stick it on the "can," and you've grounded the airplane, period. If the airplane has unresolved discrepancies, then it's no longer in conformance with it's type certification and approved data as ammended.
It's no longer airworthy.
The old airline standby question applies, even when not talking Part 121. You want to rent your airplane, and a nav light is burned out, what do you do? It's day, VFR, you won't be using the system. Can you go? Intuition says yes, but what about legality? Seems a small issue, but then that's the point.
Forgetting the issue of weather the equipment is required under day VFR, night VFR, or under IFR...was the aircraft certificated with that equipment, or was it later installed by means of a field approval or STC? Then it's now required equipment, unless you have a minimum equipment list that preapproves it's inoperative condition.
You now need to get it fixed, or make it's condition acceptably altered. Use of 91.213 does this; it prescribes a method by which an inoperative component may be altered in a manner acceptable to the administrator, in order to make the components legal.
A comment was made earlier about deactivating inoperative components. This isn't always as easy as it sounds. First one must determine if there is any manufacturer literature that regards the matter. Simply covering the attitude indicator may not be enough. You need to understand the system thoroughly. You need to be aware that often deactivation and placarding in accordance with 91.213 must be done by the holder of a mechanic certificate (A&P), as appropriate.
The issue of an inoperative attitude indicator was brought up before. Simply covering it may be scarcely enough. As airflow is typically through the attitude indicator and then the directional gyro, an inop or failing AI may and often does directly affect the DG. You now have the consideration of deactivating the vacum system; you may be looking at a pump issue, and you can't simply remove the pump in most cases. It's also appended to the engine via the accessory section. This raises the issue of potential engine complications (drive damage, garlock seal leakage, etc)...simply putting a note over the attitude indicator isn't going to cut it.
Neither is removing the attitude indicator. One could do so, but then open lines leave the vacum system sucking unfiltered, unregulated air. The entire system is contaminated. You could connect the remaining lines, but you have just made a major alteration to the system, requiring a field approval and a Form 337. A fine not to exceed ten thousand dollars comes with that one, usually applied to the owner/opeator, and a certificate suspension for you. Revocation if it involved passengers and/or safety of flight, in some cases.
The point is that it's not a light issue, at all. Nor a simple fix, in many cases. In addition to the above, in cases where alteration under 91.213 can be made by the pilot, the pilot is still fully responsible for adherence to Part 43, all applicable maintenance and continued airworthiness publications for the airplane and components, and industry standards such as AC 43.13.
On the subject of Administrative action...this isn't a test for knowledge of aircraft airworthiness. This is enforcement action taken by the FAA. A letter or warning or a letter of correction is an administrative action taken by the FAA that's a step short of seeking certificate suspension. Under administrative law, you don't have the same rights and privileges that you do in the criminal justice system; you are presumed guilty unless proven innocent. By receiving these letters, you are being notified that you have been found guilty.
The administrative letters will be placed in your record for a period of two years. If you leave the military and seek civillian work, this is going to come up. If you apply for a job and are asked if you have any violations on your record, this will surface. You can say you don't have any violations, but that you do have a letter of correction. You'll be asked why, and you'll have to admit that it's for flying an airplane in an unairworthy condition. This probably won't prevent you from being hired, but it's important to understand that a letter of warning and a letter of correction are administrative actions; it's evidence that the FAA has taken action against you, and it is a black mark.
(With the possible exception of an operation I hired on with a few years ago. During the interview with a government official, I was asked if I had any accidents, incidents, or violations. In the interest of disclosure, I told him about two letters of warning. He looked somber for a moment and then said he wasn't sure if I would make the grade. Then he added, "We usually don't hire anybody without at least three letters of warning and several violations...").
I should also add that someone above has suggested that you send a letter to the FAA outlining why you think you're in compliance, perhaps refuting the charges against you. Don't do that. Anything you say is used against you. If anything is to be done, let your attorney forward a reply, but don't do it yourself. Your only likely outcome is to bury yourself and apply evidence on the side of the FAA. Even if your letter only shows an ignorance of the regulation, it will be used against you.
Something to ponder. A Squared was correct; to address this issue any further will require the input of your attorney.