I haven't heard that Fortan is significantly faster than C, but it might be conceivable tht in certain cases it would be faster. And the key is not in the language features that are present, but in those that (usually) absent.
An example are C pointers. C pointers are used pretty much everywhere, but the problem with pointers is that the compiler usually can't tell if they're pointing to the different parts of the same array.
For example if you wrote a strcpy routine that looked like this:
strcpy(char *d, const char* s)
{
while(*d++ = *s++);
}
The compiler has to work under the assumption that the d and s might be overlapping arrays. So it can't perform an optimization that would produce different results when the arrays overlap. As you'd expect, this considerably restricts the kind of optimizations that can be performed.
[I should note that C99 has a "restrict" keyword that explictly tells the compilers that the pointers don't overlap. Also note that the Fortran too has pointers, with semantics different from those of C, but the pointers aren't ubiquitous as in C.]
But coming back to the C vs. Fortran issue, it is conceivable that a Fortran compiler is able to perform some optimizations that might not be possible for a (straightforwardly written) C program. So I wouldn't be too surprised by the claim. However, I do expect that the performance difference wouldn't be all that much. [~5-10%]