It's precisely because general relativity applies that this is possible. First, note that relative velocity and growth of distance between objects are distinct

It's precisely because general relativity applies that this is possible. First, note that relative velocity and growth of distance between objects are distinct concepts: Shoot two bullets at 0.9c each in opposite directions, and from your perspective, the distance between them will grow at a rate of 1.8c, whereas their relative velocity (as computed from the 'angle' between their 4-velocities) will only be 0.994c. In special relativity, that relative velocity will correspond to the growth of distance between the bullets as measured by an observer comoving with either bullet. In general relativity, things are more complicated: Curved spaces lack distance parallelism, so you can only compare the velocity vectors of the two bullets when they are located in the same place at the same time. Also, there's generally no longer a canonical way to decompose spacetime into spatial slices across which you can measure distances. Now, you can still define a relative velocity through parallel transport along a path connecting the two objects, and in particular the path of a photon emitted by a distant galaxy and observed by us. This will in fact recover cosmological redshift as a generalized Doppler shift. If defined this way, the relative velocity goes to c as you approach the cosmic event horizon, hence you'll never observe relative velocities larger than c. However, while there's no canonical spatial slicing in general relativity, in Friedmann cosmology specifically, a preferred spatial slicing does exist: The one where the universe looks homogeneous and isotropic and the same amount of time will have passed since the big bang (as measured by an observer following the Hubble flow). This allows us to define the proper distance (at constant cosmological time) between astronomical objects, and the growth of this distance is what's known as 'recession velocities'. These velocities go to c at the Hubble sphere, which doesn't really have any particular significance: We can see galaxies that were located outside the Hubble sphere just fine (though as time goes on, the Hubble sphere will approach the cosmic horizon asymptotically).