The idea, here, is that, suppose you had a neutron star that, at rest, was stable, and had a size only a few centimeters larger than its size as a black hole. Now imagine that it is orbiting another star, and that it's velocity relative to us is changing. If we were to measure the size of the neutron star we would, in principle, see its radius changing from being slightly smaller than it's black hole radius, to being slightly larger than it's black hole radius. Wouldn't that mean that, just on account of it's motion, it could be oscillating in size and during half its cycle, it can escape being it's own black hole? This would mean that an object could somehow escape becoming a black hole just by moving fast enough.
The problem with this is that, it is not what distant observers may see that defines whether an object has become a black hole or not. It is the experience of someone falling into this object that counts. This is similar to the issue, also present in special relativity, that it is only the experience of observers in a 'proper' reference frame that establish the invariant qualities of physical laws. For our neutron star, if our astronaut attempted to land on its surface and signal to a distant observer, they would first have to match the orbital velocity of this neutron star. In that reference frame, the gravitational field of the neutron star determined by general relativity, would look perfectly ordinary for a massive, compact object slightly larger than it's own event horizon. Sending signals to the Earth, they would be received with two 'shifts'; one due to the Doppler motion, and the other due to the gravitational redshift. The latter would be constant in time, while the Doppler shift would vary periodically as the neutron star orbited its companion. The distant observer would have to make TWO corrections to determine lengths and time intervals near the neutron star's surface, one due to the velocity difference (special relativity) and the other due to the difference in the gravitational fields which cause optical distortions. When made, the observed size would be seen to always be larger than the neutron star's event horizon. In fact, since general relativity INCLUDES special relativity, it cannot fail to give the correct, logically-consistent, results regardless of the motions and fields involved.