As someone who was in the journalism business for years, I suspect that USA Today is the default paper of choice for most of Amtrak's LD sleeper routes, with the NY Times probably the BC choice along the Northeast.
You probably only get a local replacement for USA Today when the LD trains during early morning hours find themselves in areas where the paper does not circulate promptly. USA Today is printed in a lot of locations nationwide; they are largely Gannett Corp.-owned local papers which can receive microwave transmission of USA Today pages from its newsroom in Alexandria, Virginia. In regions where there may not be a nearby Gannett-owned paper, USA Today may not arrive until the afternoon.
However, that doesn't explain why the Starlight loads the Sacramento Bee on no. 11, though no one should complain; the Bee is one of the few local/regional papers left that actually contains substantive national and world news, as well as arts and entertainment, partly because it is a flagship paper of the Knight-McClatchy chain.
And while we received the local Whitefish, Montana paper on the eastbound EB a couple of years ago (USA Today the second morning), I walked to the news boxes across the street from the station during our stop and found that morning's Wall Street Journal for sale! It was great, though I've never figured out how the Journal--which contracts with local papers around the country to print its editions from microwave transmission--got the paper to such an isolated outpost. It does say volumes about the demographics of the Whitefish area population that the Journal endeavors to do so.
The NY Times is available widely across the nation these days through printing arrangements similar to those of the WSJ and Gannett. I doubt Amtrak has any problem procuring the Times for its Northeast BC and LD routes. In fact, on one Vermonter run, there were numerous copies of the Times available for every day of that week, a telling comment on the declining popularity of print for anyone under 40, or 50?