That is interesting. One one's person is not "in carry-on baggage"-- I imagine the intent of this rule is to keep firearms out of the passenger compartments of the train but if that is the case, it doesn't say what it means. (It is always a good idea for a rule to say what it means).
There's a wider context to consider. The quote above comes from a page describing the procedures that must be followed if one wants to transport firearms in checked bags on Amtrak. The quote is an aside that occurs during a discussion of how checked baggage works. Apparently, there are some Amtrak routes that don't have checked baggage, and if one's itinerary includes one of those segments, then one can't transport firearms at all ... since that would put the firearms into the passenger compartment, where they're forbidden.
It's almost a throw-away quote as an aside ... "well, since firearms are
obviously forbidden inside the passenger compartment, if your luggage can't stay in the baggage car the whole time, you can't check the firearm".
But I agree: it would better if one could find an explicit rule addressing the situation.
Obligatory disclaimer: I've ridden Amtrak exactly once in my life, and I didn't have a firearm with me, so these are merely uninformed opinions ...