In fact, I don't believe you so much that I'm willing to say you're full of shit. No compiler capable of both C++ and C will be twice as fast renaming the file to C
I agree it shouldn't really matter if there's no C++ features in play, but I suppose third party headers could bite you if they use #ifdef __cplusplus to guard optional C++ extensions on top of their basic C interface. In that case the compiler could be dealing with dramatically more complex code when you build in C++ mode.
Maybe it is similar for the same compiler (but one should check, I suspect C could still be faster), but then there are much more C compilers. For example, TCC is a lot faster than GCC.
tcc is 8x faster, twice as fast isn't doing it justice.
As for the header thing, that'd could potentially be true if the compile time was something like 450ms -> 220ms, but why bother saying it when you're only saving a few hundred milliseconds