You should read your sources.
So I followed the link for your 'proof' that highspeed rail has higher CO2 emissions than traditional transportation methods.
In the methodology section of the report, they state plainly that because of the scope of the report, they cannot look at CO2 reductions based on the transport energy source or propulsion type, and instead use average CO2/energy cost in order to make an apples to apples comparison. Thus, the report does say that, for instance, HST, MagLev and Air have about the same energy requirements, and if we were using averaged fungible fuel sources, they would have comparable CO2 emissions. The flaw in this is that Air travel requires combustion engines - direct CO2 emissions - whereas HST or MagLev rely on electriciy, which can be generated via zero carbon methods. So while you can argue that the two have similar ENERGY requirements, it is entirely possible for HST and MagLev to be carbon netural.
You can accuse me of 'cherrypicking' by comparing renewably generated, zero carbon energy sources for HST vs jet fuel for air travel. However, the fact is Air travel can't claim carbon neutrality until their onboard power source and/or propulsion system changes. Meanwhile, HST can.
Thus, it is NOT a myth that rail has lower carbon emissions than air travel.