From my understanding of the Amtrak law which isn't that great because I am not a lawyer I believe the KCS is excluded. I want to say it is for railroads that handed their passenger services over to Amtrak which would exclude the KCS because they dropped passenger service in 1969 two years before Amtrak was founded, and one year before the legislation that made Amtrak possible was written.
Fun fact the last Pullman-Standard private railroad order was for the KCS in 1965 for new coaches. You can ride these cars today on NCDOT's Piedmont.
Of the other railroads that didn't join Amtrak in 1971 there were varied reasons for their refusal.
Georgia Railroad: They continued to operate a mixed service using one or two Budd coaches (with two Budd Sleepers in reserve) in their freight train until 1983. The reason they kept the service up was because they did not want to potentially lose their tax exemption on the rail line. While passenger services weren't mandated for the tax exemption there was ambiguity in the wording of the Georgia State law so they decided the best course of action was to let sleeping dogs stay asleep. So they continued to run daily except Sunday mixed service on their mainline, and branch lines. When Seaboard came offering to buy the Georgia Railroad they no longer needed the exemption so the trains came off.
Rock Island: The reason they didn't join Amtrak was because they couldn't afford the initial buy in for Amtrak which was 4.7 million. So they were mandated to keep their trains running until 1976 and somehow kept them running till I want to say 1978.
Southern Railway: This one is rather interesting because at Amtrak Day they fully controlled the much smaller Central of Georgia. Central of Georgia joined Amtrak and discontinued their services while the parent was left with their remaining services. Southern ran until 1975 the Southern Crescent, Salisbury-Asheville, the Piedmont (Day Train DC-Atlanta), and a remnant of the Tennesseean (Lynchburg-DC). They continued running the Southern Crescent until 1979 which in itself was really a merger of the well known Crescent Limited (originally via Montgomery and the L&N), and the Southerner (All Southern route via Birmingham). The Southern Crescent was Tri Weekly west of Birmingham and included a transcontinental sleeper to Los Angeles. The Southern Railway saw the value in passenger trains as public relations as well as they thought they could run a far better train than Amtrak. Claytor also didn't want to allow another entity onto their tracks from what I have read.
Rio Grande: I believe the reason the Rio Grande Zephyr stayed on the timetable is because they did not want another operator running on their railroad. At one point that line was a mainline before the UP/DRGW/SP Merger when most traffic shifted to the easier line over the Rockies in Wyoming.
Soo Line: They operated a mixed train until 1987 or 1989 between Sault Sainte Marie, MI and Neenah, WI strictly because they were required to by the states it operated thru. The Soo Line did the best to discourage passenger traffic though as it made a nocturnal trip leaving at the wee hours of the morning, and only allowing one ticketed passenger per day.
https://www.chicagotribune.com/news/ct-xpm-1986-02-24-8601140463-story.html
Reading System: The Reading would have been permitted to enter Amtrak and off load the Crusader (Newark, NJ-Philadelphia, PA) but chose not to because they couldn't afford to join. All that is left of this service now is the West Trenton line of SEPTA.
Railroads that almost stayed out of Amtrak
Santa Fe: It has been widely reported that had the Santa Fe been allowed to discontinue the San Fransisco Chief, and the Grand Canyon that they would have stayed in the passenger business. They did not like the idea of another company taking over their branding. Santa Fe even took the name Chief away from Amtrak so the Southwest Chief became known as the Southwest Limited for a long period of time till the Santa Fe was pleased with the standards Amtrak was using. The plan was for the Super Chief/El Capitan and the Texas Chief to continue operating. The Texas Chief and the Super/El would have departed and ran together until Kansas City ala the City of Everywhere on UP. It is rumored that the government had it's eyes on Santa Fe's well maintained coaches and cars for Amtrak and prevented this future from happening. Santa Fe was perfectly fine with running it's own trains till the very end and maintained their standards.
Seaboard Coastline: Seaboard like the Santa Fe also had very high standards until the end and their ridership did decline towards the 60s but not at the same rate as the rest of the class one railroads. Had Seaboard kept their trains they might still be running today. The Florida market has always been a very strong market for passenger trains and up until the 1990s the trains were regularly running 18 cars.
The railroads that desperately needed Amtrak were the Penn Central, Southern Pacific, Rock Island, and a few of the smaller operators.
