Animal control authorities demanded the animals be turned over to them under threat of a warrant, and then the woman was arrested for the medication she gave them while housing them, since she is not a veterinarian. The press release from the district attorney goes to great lengths to point out that the official county shelter would have housed the animals during the flooding for free, and also says the woman had previously been "censured for the unauthorized practice of veterinary medicine."
All of that may of course be true, and perhaps some animal owners would have been wiser to take their pets to the county shelter or to check that it was open. It might also have been wiser for the woman herself to try to reach the shelter rather than house and medicate the animals herself.
If so, then the smartest thing for the county to have done would have been to issue a strong statement to that effect, warning people against possible substandard shelters who might offer unlicensed medical care. The second wisest thing, counter-intuitively, would have been to have followed through on the charges in some way -- a citation, a fine, community service, whatever. That would have shown they took the matter as seriously as they said they took the matter. But by charging her and then dropping the charges just a few days later, they look like bullies who demonstrated their power in order to keep folks in line who might want to help animals.
In essence, the county has walked into this situation and said, "Dis is a nice place! It'd be a shame if anytin' was to, ah...happen to it."