Yes, I think this is essentially what they intend!
To be a bit more specific, the unit cell contains one atom at [0,0,0] and another at [1/4,1/4,1/4].
Now consider a longitudinal wave in the (1,0,0) direction. For such a wave, the entire plane of atoms with coordinates [0,a,b] moves together in the (1,0,0) direction (changing position 0 to some small x), and similarly the entire plane of atoms with coordinates [1/4,a,b] moves together. You can think of these planes as being masses. With a bit of geometry you can see that the springs between the planes (the spacings etc) are identical.
Now consider the (1,1,1) direction. Here there is a (1,1,1) plane that cuts through [0,0,0] and there is another parallel plane that cuts through [1/4,1/4,1,4]. The next plane will cut through [1/2,1/2,1/2] -- even though there is no atom at the position [1/2,1/2,1/2]. We are meant to conclude that (even though the spacing of these planes is uniform) the spring constants in this direction actually alternate! (It requires looking at the crystal carefully to see this though!)
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