Learn English – Figuring out what’s wrong with the sentence

The primary difference in the forms of the two sentences is that the first one has "eats... reading..." and the second one has "was making... talking..." It thus seems that the first sentence—punctuation aside—can be read only as signifying

He always eats breakfast [while] reading the paper.

whereas the second sentence—again, ignoring punctuation—can be read as meaning either

She was making sandwiches [while] talking with her daughter.

or

She was making sandwiches [and] talking with her daughter.

So perhaps the comma is there to signal a dropped and and to emphasize the parallelism between "making sandwiches" and "talking with her daughter," both of which attach to the word was if an implied and is at work. I certainly don't see the argument for putting a comma after "sandwiches" in the second sentence as being any stronger than the argument for putting one after "breakfast" in the first, if the point is simply to mark the absence of the intended word while in both cases.

Still, I'm at a disadvantage in trying to work out the book's reasoning because my preference would be to include the missing while in the first sentence and the missing while or and in the second sentence—and if you do those things, neither sentence needs a comma.

Prepositional phrases may be attached to either nouns or verbs.

A prepositional phrase attached to a noun will take commas following restrictive/non-restrictive logic (e.g., "her death, in London, was shocking").

However, a prepositional phrase attached to a verb never takes commas, which is why "He died in 1989, in a car accident, in Detroit" is incorrect, because the prepositional phrase "in a car accident" is attached to the verb "died."