The use of "から", specifying "噴火した所" as a starting point, is especially appropriate because it reflects a certain part of reality pertinent to the discourse, namely that the hazardous emissions will spread from the point of eruption outward, toward the surrounding area, and that consequently people will conceive of the no-go zone as following this direction, though area (or distance) does not have direction in itself.
To be sure, had the writer used "に" instead of "から", there wouldn't be any problem at all. It would make perfect sense and sound natural in the context.
But designating 噴火した所 as the point of origin and therefore assigning an outward direction to the range of no-go zone by using "から" makes for a more satisfying read, because it nicely fits our perception of the relevant part of the reality. I think.
Particles we can make use of to talk about near-ness and far-ness with reference to a given location X are: から (marks X as starting point), まで (marks X as end point) and に (unmarked, or end point-ish?), with the exception that Xに遠い feels weird to me.
- Xから近い Xまで近い Xに近い
- Xから遠い Xまで遠い ?Xに遠い ( ?Xに遠い is very uncommon and possibly ungrammatical or nonstandard)
My uneducated impression is that when the "direction" of distance (that is, starting-point-ending-point stuff) is unimportant, we tend to use "に" for "近い" and "から" for "遠い" (for which "に" is not a real possibility). I also suspect that some of the time people's choice of particles in this regard gets a bit arbitrary or at least is not dependent on their respective meanings.
I looked in 現代日本語書き言葉均衡コーパス (BCCWJ), just to make sure there aren't any real instances of "Xに遠い", to find these entries below, which all seem to be legitimate cases of the construction.
- 山間部や海に遠い地方の人たちは塩鯖で海の味を食膳に載せたのでしょう (渡辺一枝,1940)
- 太陽からの熱により気体になりやすい成分（揮発性成分という）は蒸発しているが，太陽に遠い部分では，固体（氷）として存在している。(from some school textbook)
How should I re-label its status? "Out-dated, now very weird, though possibly not as weird in the past"?