You are pretty much on the right track although you have touched on my pet hate: The phrases Bulk-Up and Tone. These are utterly meaningless phrases. Your muscles can either ‘grow’ (Hypertrophy) or ‘shrink’ (Atrophy). They cannot bulk up, neither can they be ‘toned’.
Back to the question
Hypertrophy is almost universally accepted as the result of repetitive movement against substantial resistance. As you point out I doubt that the breathing head turn would fall into this category.
As Atticus Finch points out, these atheletes train hard outside the pool with weights to increase their strength, and the shoulder exercises which would translate into stroke power in the pool will definitely include the major muscles of the neck.
Finally, it is worth noting that not all physiological attributes are a result of training or performing in a specific sport or activity. For example does playing professional basketball make you tall? No, obviously the people with innate or genetic predispositions will flourish and be able to perform better.
I would guess that the ‘strong necks in swimming’ is a combination of the 2 processes above.