His logic is wrong. It's not because they are objects, it's because std::sort and friends are function templates. They know what they are calling at compile time. Templates allow for compile-time polymorphism like this.

Because of compile-time polymorphism, you can pass in prvalue function pointers and objects alike and the compiler will be able to inline.

C doesn't have templates, therefore it doesn't have compile-time polymorphism, therefore it's much harder for the compiler to inline.

Compilers like GCC and Clang can inline in some runtime-polymorphism circumstances. See -flto and -fdevirtualize.