I can't find anything online that suggests air is ever cleaner than rail. The discrepancy is a factor of 20ยน, so it would be surprising if circumstances overcame that, unless you are traveling across an ocean.
For idealized shorter range distances (300~350 miles) I've seen claims of 2x or 2.5x, sometimes up to 5x, but that's using full LCA, not just fuel per passenger mile. The embedded energy in ROW and track are significant, and it doesn't scale well (capacity wise) compared to air travel.
In favor of hsr, but still with some big assumptions and limited distances. The fuel factor is huge, but still relatively comparable between modes, and it's all heavily dependent on % of empty seats.
95% is extreme, but it's usually assumed to be in the 55-65% range for generic civil infrastructure, not hsr specific. Compared to that hsr is heavy on concrete and steel, so would be higher.
Embedded rail infrastructure costs are calculated based on near track capacity (amortized over 30-50 years, which is generally correct for civil projects), and typically near train capacity. Empty trains are much worse than empty airplanes, and if ridership isn't projected accurately pulling a train from a route doesn't reclaim any embedded costs of the track or row, while airline infrastructure can be completely reallocated. Multiply a miscalculated capacity by 50 years and it turns into a big number.
I'm about 2/10 so far on finding these papers I'm looking for today, but this one at least addressed ridership implications for the California project in terms of LCA.
And here's one comparing air to hsr in Europe, showing only 3%-20% gains by shifting passengers from air to rail, based on existing infrastructure, but using LCA assuming a %50 recyclable rate for rail.
[1] https://en.wikipedia.org/wiki/Environmental_impact_of_transp...