From the web site:
"Folding bicycles may be brought aboard certain passenger cars as carry-on baggage. Only true folding bicycles (bicycles specifically designed to fold up into a compact assembly) are acceptable. Generally, these bikes have frame latches allowing the frame to be collapsed, and small wheels. Regular bikes of any size, with or without wheels, are not considered folding bikes, and may not be stored as folding bikes aboard trains.
"You must fold up your folding bicycle before boarding the train. You may store the bike only in luggage storage areas at the end of the car (or, in Superliners, on the lower level). You may not store bikes in overhead racks."
Don't know how small an S&S coupled bike gets down to, but if it fits in a case that does not exceed the max. measurements for general carry-on baggage 28x22x14), what's the rationale for excluding them? Wait. It's Amtrak. Never mind.
BTW...I probably ride Amtrak more than most. I have seen a lot of carry-one bags that exceed the max. size.