Could you elaborate on this? The only thing I've heard about this before is that many of the Native Americans have dramatically unpleasant reactions to alcohol.
Considering that a good number of the Alaska State Troopers use aircraft to travel in their patrol area, I'd say that's pretty likely. In Florida, the sheriff's dept. books every single arrest in their county no matter which agency makes it, even in very large cities. Things are done different in every state.
Another thing, I know several people from Alaska (including a former Alaska LEO) who've all repeatedly told me how common weapons are up there, and how little the cops care about them, even things like illegally carried switchblades or open carried guns when they were contacted by LE while engaging in stupid teenager antics. One lived in an apartment building in a large city where an angry drunk was trying to kick in the door of an apartment he thought was his (there's a comical story behind it), and the person inside shot & killed him through the door...LE showed up and didn't even run the serial # of his pistol or temporarily take the gun; no charges filed or anything, they took the situation at face value and let him go back to sleep.
If the Troopers in this case did in fact try to drum up some charges over something legal then I think that's an abuse of power, but from everything I've ever heard of that state, she must've been doing something extraordinarily stupid to get the kind of LE attention she allegedly got.
Native Alaskan's have extremely high rates of alcoholism for some reason. That much is certainly true.
In regards to your last paragraph, it seems that the woman's extraordinarily stupid act was no instantly subjecting herself to the trooper's wishes, instead preferring to continue her legal activity.