Yes, notice that even if you don't know what kind of coordinates are allowed in GR, from SR you know points of equal time coordinate must form surfaces, so any object with a non-zero 3-volume cannot lie on any such surface.

As an aside, it really grinds my gears when I see popular science articles describing astronomical observations as being "in the past". Pretty much by definition everything that affects us must be in our causal past light cone, so in a strict sense that statement doesn't say anything at all. But it does try to say something, it tries to make astronomical observations seem different from everyday observations. In particular, people have this intuitive but non-physical idea on "now" happening around us, and these articles try to give the impression that "now" in those faraway astronomical objects is different, as if the notion of "now" (either here or there) would be a real physical thing, when only the observer's now is physically meaningful. They implicitely talk about THE faraway "now" when the whole point of GR is that there isn't a unique such thing.

Articles get this backwards. The fact that light comes from the past is true both for astronomical phenomena and for everything else, that's not what's interesting, what's interesting is precisely that coordinate mappings can't be unique and by mixing ontologically different categories of "now", they obscure this idea further.