But I'm sure you know more and better than the designers of the C# and Java languages.
The term that Anders Hejlsberg used was "C-like", which is a much weaker claim than "C-based" or "C derivative". I don't know that James Gosling claimed any similarity to C except for syntax.
I'm sure C++ is also not C based by your definition.
Of course not. C++ and Objective-C are absolutely C-based, in that they share semantics and are even backwards compatible with C. It would be fair to place D and Rust in the C family, too, as well as more obscure languages like NXC, Cyclone and Lite-C. (And that's not counting C's ancestors and close cousins like BCPL and Bliss.)
C# superficially looks like C, in the same way that Indonesian superficially looks like Latin. But Rust is a closer relative to C in the same way that Russian is a closer relative to Latin.