[clang] Don't include C++ Standard Library headers when -nostdinc is used

This is a follow-up to 53c98d85, which made the same change but only
for GNU. It seems that we should try to provide a consistent behavior
across all targets.

This fixes an issue where clang/test/Driver/nostdincxx.cpp would start
failing on non-GNU targets because that test was too loose in its checks.
It would only check that 'file not found' was part of the error message,
but didn't ensure that the file we had not found was <vector>.

Differential Revision: https://reviews.llvm.org/D138062