Couldn't be further from the truth. Due to cybersecurity regulations, government technology access lags multiple generations behind civilian world tech.
I have seen a lot of bleeding-edge medtech. It is all using "AI" but it is DEEPLY STUPID and most of it is very bad at its job. However, some of it is very good at doing the jobs of some medical staff better than medical staff: in the next 10 years robots will count and dispense your medications better than nurses (because unlike nurses, they never get tired or malicious). They'll do all the fetal measurement for ultrasounds. But human judgment style tasks are genuinely outside the reach of medical technology (or indeed any technology) at the moment.
Your first notification that AI has breached this barrier in any area will be that the stock market goes bugfuck insane for months on end. Once AI can actually have better-than-human judgment capabilities based on incomplete information, it'll be used to make financiers money before it's used for anything else.
The idea that G-men have labs full of secret tech is based on Cold War era spending when the government did the best tech work in the world and wouldn't entrust it to private corporations because of potential surveillance threats from Russia. But since the 90s that has completely reversed, the government uses procurement processes to obtain technology that basically ensure it is created in the most cumbersome way possible, by "old guard" companies that move slowly and incrementally rather than by breakthrough.