Yes, there is some truth to that, in that either type of device is optimized for what it is sold as, and the other capability is secondary. However, as you note, he is a salesman. He is up on the most current advances in both fields and ready to converse with a customer interested in those latest features. In short, his advice is most appropriate for a high-end customer. If you are a basic customer, you need to consider some of it FYI only.
The state of the art is advancing quite a bit as far saving digital images. Moving images are just strings of still images, so the two technologies are converging. And if your needs are basic in either area, the secondary capability may be enough for you.
So
I wasn't saying tell your relatives don't get a video camera if that's what they want. I was saying, if you already have a digital still camera that can shoot video as a secondary feature, try it out, it may do what you need right now, and then you don't have to worry about borrowing the video camera (as much anyway).
If you don't then never mind.
Personal anecdote: My wife doesn't have any background in photography; I do. She rarely takes pictures but complains when the family doesn't have pictures. Last year she started complaining as well that we didn't have a video camera; I didn't want to start dealing with a second device for her to complain about me not using enough so I pooh-poohed her. Then our digital camera broke and we got another one; it has video capability (640x480x30fps or 320x240x60fps). I got some big memory cards, I shot some video of the kids with it, hooked it up to our TV, played it back; she got all excited. Now we carry the one device around, usually I shoot still pictures, sometimes she shoots still pictures, and sometimes I take a video. It's good enough to make our home movies.
(If it matters our current camera is a Canon Powershot A620.)