I believe the claim is more precisely stated as "Many C programs are valid C++ and are faster when compiled as C++" - i.e., even though the text of the program

I believe the claim is more precisely stated as "Many C programs are valid C++ and are faster when compiled as C++" - i.e., even though the text of the program didn't change, the rules for interpreting that text changed, and it's that difference in interpretation that permits better optimizations.