It seemed like the point of the presentation was really that C and C++ should be thought of as totally separate languages.
As long as that's remembered, I think the opposite is probably true: knowing C helps a lot to learn C++ (and vice versa) as opposed to learning either from scratch.
This is true, but there's a 'surface simularity' problem. It's easy to go from writing C to writing old-fashioned 'bad' C++. Modern C++ really is a different beast.
The thing is that if you're actually teaching C++ (which I have done), there's still the C parts that you actually have to teach as well that are common between both. So, if you know C, you don't need to learn those over again. I actually took a course at one job on C++ for C programmers back in the 90s and it was very well done for the time.
True, modern C++ is quite different. But, there's nothing from preventing a C programmer from starting as a "bad" C++ programmer and learning new techniques as they go.
As long as that's remembered, I think the opposite is probably true: knowing C helps a lot to learn C++ (and vice versa) as opposed to learning either from scratch.