Even though im not completely sure, where your exact problem is, ill give it a try:
Lets first think about a book lying directly on earth's surface:
First of all theres a gravitational force $F_G=\frac{m_1\cdot m_2}{r^2}$ This force does not specify which object is "the pulling one" and which object is "the pulled one" - its just a force, acting between two objects, pulling both together. Of course since the earth's mass is "sligthly" greater than the books mass, the actual acceleration $a = \frac{F}{m}$ will be "slightly" different, but thats not the point here.
What we see is, that the acceleration seems to be $a = 0$ here for both objects - so we need some force which adds up together with gravitation to $F=0$ and call it contact force.
Thats exactly the point where this little imaginary experiment comes in:
We assume theres a spring between the two objects and ask about "how much it is compressed".
From our perspective we can say it acts as a scale, measuring the weight of the book on earth. But we could as well say its a scale, measuring the weight of the earth on the book. Or we could say its just a spring, pushing the two objects away from each other with exactly $F_G$.
All descriptions are the same, we are just used to talking about a scale if one object has a relative high mass (e.g. earth) and the other has a relative low mass (e.g. book) while we are used to talk about a spring if they have comparable masses (e.g. two books).
You could as well think about the two connection points of the spring.
Which forces act on the connection point between the spring and the book?
Obviously what we are used to refer to as "gravitational force on the book" and the force of the spring, caused by its compression. 343
Since the point is not moving, both must be equal in strength and opposite in direction.
Which forces act on the connection point of the spring with the earth?
Obviously the force of the spring, cause by its compression. Since we are talking about the same spring, it needs to be the same force as before (just the opposite direction). And since this point is not moving as well, there needs to be a second force counteracting it - you might be tempted to call this a contact force, keeping the spring (and the book) from moving "into earths surface", which i would not call wrong, but lets think for a moment where this force comes from. It's basically the gravitational force from the book on the earth.
Lets think about a last experiment: Think of a stack of massless scales on earth's surface with a book on top.
What weight would the top scale measure? Of course, the weight of the book.
What weight would the lowest scale measure? Since all scales are massless, it would still measure the weight of the book, no matter how many scales are in between.
All of this boils down to one conclusion: If you have a book lying on earth's surface, there are two forces: The gravitation and some sort of "contact force" counteracting the gravitation. If we model this contact force as a spring, only one force is left to compress this spring: gravitation. From what i've read, thats the point <PERSON> is trying to make.
Of course this gravitational force acts on two objects: The earth and the book. And thats the point the experiment with two springs is trying to make.
The same applies to the contact force: Theres only one contact force keeping the objects from moving into another. But it also acts on both objects.
At the end, all of the descriptions are the same, its just a different view. 319