....and what authority does an energy company have telling you to stay off the lake?
Duke energy owns the lake bottom, the lake water, and the shoreline (they bought all the land for the lake 100 years ago). They also approve all construction within 50' of the 760' line (which is the water elevation at full pond). They used to own all the land around the lake, and when they sold it for private development, all private development had to agree to this restriction of use. We own our dock (it came with the house), Duke permitted its placement on lake water after they approved engineering and design. If we do something bad (like mess with the shoreline, or make significant unapproved changes to our dock), Duke can revoke the permit and decide not to give us a new one for a few years. That fear is normally enough to get people to treat the lakeshore responsibly - which the vast majority of people do. Over the years, they have become more restrictive with what they will approve - requiring larger lots if you are on septic - and banning further construction of boat-houses and over-the-water enclosed docks.
There is a grey area when it comes to public lake access. There are a number of public boat launches / boat ramps and Duke doesn't own them, but they work with local authorities to manage access for public safety (they are typically owned by the counties). Likewise there is a boat launch in the state park where the same situation applies - and private marinas usually have boat launches.
This is the first time in the 60 year history of the lake that Duke has closed the public boat ramps (by asking local authorities to close them). They have also asked the marinas and private property owners to voluntarily not launch boats for a few days - to minimize damage to the shoreline, and allow clean-up and emergency personnel free access to the waters without worrying about recreational users. I have to admit - since the word went out, I would say 99% of boaters have voluntarily stayed off the lake.
Sad sidebar - there are many times when emergency personnel are trying to work on the lake, and they are hampered by stupid/drunk boaters. Several times this summer search and recovery were looking for drowning victims, and despite lights flashing and dive flags waving, they couldn't keep boaters away and had to pull divers from the water. These tend to be in shallower areas of the lake (sandbars, etc) where many people congregate to party and swim - and it is dangerous for divers to be in the water with people approaching in big cabin cruisers.
I will say - I have no issues with anything Duke has done with lake management. They tend to manage things with a light touch. However if you decide you are going to cut down every mature tree on your shoreline and put in an unapproved seawall, they will happily take you to court to force you to undo all the damage - and you will lose - as several high profile cases over the years have shown. Additionally, there are stretches of shoreline that are protected for environmental reasons, and even if you are allowed to build a house there you will never be allowed to build anything along the shoreline, or have a dock.