Is moving twice in a single full expression allowed

Assume one has a function with the following prototype

template<typename T>    
std::unique_ptr<T> process_object(std::unique_ptr<T> ptr);

The function may return (a moved version of) the object that was passed to it, or a completely different object.

Is it legal C++ to use this function as follows?

std::unique_ptr<Widget> pw(new Widget());

pw = process_object(std::move(pw));

If I remember correctly, there is a C/C++ rule that forbids modifying an object more than once in a single full expression. Does this rule apply here? If yes, is there some way to express this idiom differently in a single line?

What if one replaces std::unique_ptr by the despised std::auto_ptr?