Well, the article is a little overzealous in its interpretation of the law.
Technically, the US law says you're not allowed to "disturb" an eagle without a permit (Canadians do whatever they want to them. It's not their national bird and they're no longer endangered, even in the US).
Under the law, the key definition is disturb: "Disturb means to agitate or bother a bald or golden eagle to a degree that causes, or is likely to cause, based on the best scientific information available, (1) injury to an eagle, (2) a decrease in its productivity, by substantially interfering with normal breeding, feeding, or sheltering behavior, or (3) nest abandonment, by substantially interfering with normal breeding, feeding, or sheltering behavior."
Flying a drone near an eagle, based on the best scientific information, should not, under this definition, disturb an eagle, even on a nest. Fish and Wildlife would have to demonstrate that you decreased the eagle's productivity or caused it to abandon a nest. The USFWS can often go overboard in interpreting this to mean even looking funny at a bald eagle is a violation of the law and it is often questionable if it would hold up in court.
That said, I wouldn't want to fight the federal agency when it gets its knickers in a bunch and even if you're ultimately found innocent of the charges, you're going to spend a whole lot of time and money in court just to defend yourself. In this case though, it appears the agency probably did the right thing: "The agent “opted to provide basic education,” the spokesman said."