Should one always define a copy constructor for deep copying pointers in a class with raw pointer members?

To my knowledge, in theory, if a class has a raw pointer member, then the default copy constructor will do a shallow copy of that pointer, such that when the original object is destroyed, the pointer member in the copy will have had the value to which it pointed deleted. This seems to imply that outside of the case where we want to restrict copying for some reason, any class with a raw pointer member should define a copy constructor to do a deep copy on that pointer.

I am working with a respectable third party API, and I've come across a class with a raw pointer member, but no defined copy constructor, which casts doubt on my understanding above. Am I missing something?