One should be cautious here - covering avoidable costs doesn’t necessarily mean profitable.
Yes, it does mean that particular train is profitable.
OK, look, I'm an expert on the concepts of "profit" and "loss". They're trickier concepts than most people think.
It is quite possible to have a dozen products each of which is profitable, and for the business as a whole to be unprofitable. This is, of course, the Amtrak situation.
As you note, *fixed shared overhead costs* are the reason for this. This is a very specific, and common, business situation. Each product is profitable. "Marginal profit" is the technical term. But you have to make enough total profits from products to cover the fixed overhead in order for the business as a whole to be profitable.
This is what profit and loss actually mean. And there's an important lesson for businesses with high fixed overhead costs: *you need to be selling more product* in order to defray your fixed overhead.
(The situation is particularly extreme for telecoms, even more so than railroads -- there is no such thing as a financially successful small telephone company: you need to be *big*. This is why the AT&T monopoly existed.)
In the Amtrak case, to reduce the need for Congressional subsidy, Amtrak needs to *expand* in ways that don't increase fixed costs -- more trains per day on the same route, for example.
This is something which has not made it through the heads of Congress, so that's why it's important to make the point very explicit. Each train is profitable. The business as a whole, made up of a bunch of profitable trains, is not profitable, because *there aren't enough trains*.