Why can I seemingly define a partial specialization for function templates?

Function partial specialization is not allowed yet as per the standard. In the example, you are actually overloading & not specializing the max<T1,T2> function.
Its syntax should have looked somewhat like below, had it been allowed:

// Partial specialization is not allowed by the spec, though!
template <typename T> 
inline T const& max<T,T> (T const& a, T const& b)
{            //    ^^^^^ <--- supposed specializing here as an example
  return a; // can be anything of type T
}

In the case of a function templates, only full specialization is allowed by the C++ standard.
There are some compiler extensions which allows partial specialization, but the code looses its portability in such case!