Yes, per passenger there are more emissions taking the Amtrak train than flying if you average everything out over the route lengths, but not by route ridership. There are many parts of the equation where US and Canada rail are inefficient that any improvement in service would improve the numbers to quickly take over as the greener way.

The biggest is owing to the amount of travellers. Airlines try to cram people on planes, and they are known to overbook to get as many seats filled. Cross country train travel is generally less booked outside of popular weekends and holidays. Commuter trains have a reliable number of passengers coming in and out of the city making it very efficient.

The train engine itself is capable of pulling at least 2 or 3 times as many passenger cars without a noticeable impact to the travel time. If these intercity routes were more popular and ran more often with matched demand then it would be more efficient than planes. It’s just that this power is wasted. Freight companies like to make money which is why their trains are excessively long and they move ton-miles essentially as efficiently as they can because of that.

The windy rights of ways owned by freight railroads and the fact that Amtrak/VIA can’t have their way ever because of their bullying means we’re stuck playing by their schedules. That is the case until the US or Canadian gov grows a spine again and buys one of the class 1s. A government owned freight company can better coordinate to provide the important infrastructure upgrades that would make the journey even better, faster and environmentally friendly.