These aren't different interpretations. I've pointed this out before. General relativity is simply both a geometric and a field theory (trivially, since the metric, which describes the geometry, is a tensor field). These are not mutually exclusive. In particular, pointing out that GR is a field theory doesn't negate that it still has the same coordinate-system independence ("gauge freedom") built into it. Since Kevin Brown doesn't provide a source, there's no indication where he got the idea these are different interpretations from. This is also somewhat true of gauge field theories like quantum electrodynamics, in that they can also (in a sense you'd find very abstract) incorporate geometric ideas closely analogous to those used in general relativity. For instance, the electromagnetic field (Faraday) tensor plays an analogous role in QED as the Riemann curvature tensor does in GR. So, arguably, it's really gauge field theories that are more patterned after general relativity than the reverse. Then you and anyone else who says this were proved wrong many decades ago. We can identify frames and coordinate systems near and inside the event horizon that are perfectly valid by GR's internal logic. You've never been able to point out anything wrong with them (like why they shouldn't be considered valid, or why the metric expressed in, say, Kruskal coordinates shouldn't be considered a valid metric or solution to the Einstein field equation). The way I see it, the only way you can get something even close to your frozen star interpretation is to take a black hole geometry manifold (such as the Schwarzschild geometry), work out where the event horizon is, and arbitrarily cut the manifold off there and say everything beyond it "doesn't exist". In that case, you'd still have a manifold that was compatible with the Einstein field equation, but most physicists and mathematicians would tell you it was incomplete, and you'd have the odd implication that matter and astronauts could literally disappear off the edge of spacetime in finite proper time.