That is exactly right... It is like they are assuming that by knowing C, then implicitly they know C++. That's tremendously wrong and they will notice that as soon as they work on a non-so-small project.
But, what about a C++ programmer who knows the quirks of C?
Not quite. It's fairly common in an embedded world for a system engineer that uses C for low level programming and C++ for application/UI level.
Why do you say that?
By definition C++ is a different language (contrary to Objective-C that was "an extension to C"). It encompasses a lot (nearly all) of C but introduces also new concepts. For example and besides the evident OOP features, all the different types of casting, use of IO stream, default parameters...
People who know both languages well, also know that they are different enough to not be casually lumped together like that.