Gravitational time dilation is not a physical invariant. It's a very heavily coordinate-dependent quantity. The gravitational time dilation factor is not only observer-dependent but also depends on the choice of a (generally arbitrary) simultaneity convention. Even gravitational time dilation going infinite doesn't necessarily mean anything. Accelerating reference frames are a well-known example where gravitational time dilation can become infinite and even negative, purely as a mathematical consequence of how these reference frames are defined. And why would I want to do that? Surely it's how the metric is defined and used in the theory that should matter, and not what it's called. (You know appealing to etymology is a logical fallacy, right?) And? The times accumulated by the clocks and the ages of the twins won't be the same. (Also, not everything is a light clock.) The picture you linked to is an illustration of the rubber sheet view. As you should already know, that is at best a highly inexact and in some ways misleading analogy for general relativity. That picture isn't new, by the way. It's probably older than I am, and every introductory and popular science-level exposition on black holes seems to include it. If it's actually known to be accurate in some important and relevant way, you should be able to cite where that was demonstrated in the scientific literature.