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.
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
If those made-up numbers were true, they would be very significant and an argument in favor of keeping the code in C
1990's compilers were also super fast, they only did optimisation for size, speed, constant propagation, and little else.
Zero code motion, loop unroling, code elision, heap via stack replacement, inlining,...