I've also never seen anyone say that Rust is closer to C than C++, that also seems weird.
Person 1 says, “Zig is a viable C replacement, Rust is a C++ replacement.” Person 2 responds, “Rust is absolutely a C replacement, Rust is so much more simple than C++, that they should not be compared. That simplicity, which is much closer to C than C++, is why Rust should be viewed as the ultimate C replacement.”
So, it’s not a clear cut statement that Rust is closer to C than C++. However, I certainly have taken that as the argument in most discussions I have seen.
Rust needs to compete with ISO C++ current, not ISO C++98.
In any case, C++20 has Concepts, which where used clear up the template error problem.
That said rust is pretty different from c++. Most people don't compare rust to c because c is so heinously unsafe and rust being the polar opposite. Ironically, rust was indoctrinated as the second supported language to the Linux kernel, alongside C. So they have that in common...
I wouldn't make too many assumptions about the rust community, they are pretty nice smart reasonable people who tend to write c/c++ for work...