No, it's both field of view and the background being more out of focus with the longer lens.
We can fairly easily choose a suitable background, but need the longer lens to throw it out of focus to a greater degree. I believe more photographers are concerned with creatively using a soft focus background to hint at the environment, rather than using as plain a background as possible.
In the eggbox example, the lawn area is uncluttered, yet the advantage of throwing it more out of focus is visible.
The depth of field is only relevant to the subject in focus, with the scene in front and behind being thrown out of focus more rapidly by the longer lens.
Sorry to disagree but that's not what I'm seeing. The background is not more
out of focus with the longer lens, as any depth of field calculator will prove.
The increased 'isolation' with the longer lens shot is down to the narrower field of view and the less cluttered background, as depth of field remains the same in the two pictures, f/number for f/number. To think of that slightly differently again, it's a perspective effect due to the increased subject distance (hyperfocal distance has no bearing).
But whatever, if you take a picture with a 50mm lens, then move back and reframe the main subject identically with a 200mm lens (as you have done with the egg box) then at a given f/number the depth of field will be the same.
It's easy enough to prove for yourself, by setting up two pictures as you have done, noting the focal length, f/number and focus distance settings, and reading off the depth of field from an on-line calculator such as:
http://www.dofmaster.com/dofjs.html
If you want to have a go at that, make sure you are comparing apples with apples (and not eggs LOL). That is, exact focal lengths are often not what is marked on the lens barrel, and you need to measure actual focusing distances from the front of the lens (not the focal plane, which is what focusing scales read) as that's how most DoF calculators work, and different lenses are obviously different physical lengths. So it makes exact comparisons quite difficult but you'll get close enough to see that what you're saying is not true. Focal length makes no difference to depth of field in this case, and so it must be a field of view effect - an illusion, if you like.
All of which must be taken in the context of depth of field being an approximation by nature, and apparent sharpness, or lack of sharpness, is a subjective thing and a pretty vague one at that. However, it is important to know that you do not automatically get less depth of field with a longer focal length lens, or more depth of field with a shorter lens. There are other factors at play.
NB The bit about hyperfocal distance is a red herring. If you increase the circle of confusion in this equation to replicate how more distant subjects becoming increasingly out of focus, the relationship between the two lenses remains the same (as you would expect).
