I think the US military has been training is US cities for decades, and sometimes you know what's going on, and sometimes you don't. It's because they operate, or are assigned to operate in major cities all around the globe. What better place to train than our own cities?
The one example with which I am personally familiar involves a special forces sniper school I attended many years ago. The final phase of the school involved a number of field training exercises, or FTXs, a number of which were urban in nature. In one we had to infiltrate an urban environment at night undetected, spend three days in a building without being caught, then at about 2am one morning take live rifle shots in an intersection. The target was surrounded by sandbags that were quickly put in place by support staff, then just as quickly removed once the shots had been taken. We had to exfil the area carrying everything we had produced in 3 days, including bags of poop, again without being seen.
This wasn't training against local citizens, it was training for real world specwar missions in other countries.
Now, I suppose someone somewhere could try to order those soldiers to turn their skills against American citizens, and maybe a few would, but that has nothing to do with the training that we see from time to time. If it's being done right, this kind of training takes place all the time and you never know it. The real fear I have is the kind of politician that would try to turn those skills against us. That is what you must watch out for, that is the threat, not the guys training to do their job.