Yeah. Pretty much underlines why I'm not a big fan of planet skyboxes... they pose too many limits. 
Skyboxes have no limitations. The imitate reality as closely as you make the 3D scene to be.
Background bitmap planets have
exploits. They enable you to show egregiously falsified views of planets.
Let me elaborate:

Here is a planet as it is seen from four points (P1-P4). P1 is the furthest, P4 the closest point.
The apparent diameter of the planet varies depending on the distance.
As you draw tangents to the planet to determine the apparent diameter, you notice that the lines obviously also limit the area that is visible to the view point. Player in P1 is able to see nearly full hemisphere. The line crossing the area visible to P3 is about 1/3rd of the planet's circumference, for P2 it is one quarter of the circumference, and for P4, the line through the visible area is only about 1/8th of the planet's circumference.
Now if you consider that when you change the
apparent diameter of a planet bitmap, you're doing
nothing at all to change how much area of the planet's surface is visible. It's still a static
image of the planet
as seen from the original rendering distance.
Skyboxes automatically take care of this. Not so with re-scaleable planet bitmaps. This is my main issue with skyboxes that essentially take any high-resolution planet image available and just scale it to high apparent diameter in the game. Essentially it's like taking a photo of a car, resizing it and then saying that because the photo is larger it was taken from closer.
Now, regarding the seemingly insane texture resolutions, let's take a look at what sort of area of surface is visible in a single skybox render which has 90 degrees field of view:

The red area is the actual area visible in the "down" render which is the most critical one regarding texture stretching. It's easy to see from here that the visible area is only approximately 1/24th or so from the entire circumference of the planet from edge to edge.
Practically, this means if you have equatorial resolution of 21600 pixels in the texture, you will have 900 pixels to stretch from one edge to another. If you use 4096^2 resolution, that means the texture is stretched by factor of four. That's a rather heavy amount of blur you get to that texture there.
This is basically the reason why such large textures are needed and useful. For skyboxes where the planet is further from the player (and, subsequently, has lesser apparent radius) much smaller textures are sufficient.