It's a little more complicated than that (and the original post is a ridiculous oversimplifications with the intellectual level of a 5-year-old, if that much).
It's down to how much do each of us owe to the Society we grew up in and the Society we live in (if not the same) and thus how much do we have a moral duty to pay it back when called upon it to protect said Society.
Different people will decide differently on those things and thus determine in their own minds what they think their "duty" is.
Then of course, on top of this there's also the whole "protecting my family", "fight alonside my friends", plain old "warrior spirit" and such motivations on one side, as well as "having to stay to work to feed my family" and such on the other, but that's not really to do with "duty" and "moral".
In this specific case there is also the HUGE moral element that they're paying to avoid the draft, and those doing so actually have money, so they're likelly bigger beneficiaries from Society than those who can't afford to make such payments, which brings in a massive element of injustice (one might make the case that the richer the person the more they have a duty towards the Society that made the and kept them thus).
Ultimatelly the draft itself should include some elements to make it fairer (and it does, up to a point, thinks like not drafting poor people with lots of kids - who need to earn a living for their family - or people who don't have the local citizenship - who likely owe much less to local society than the locals) but in this specific case it absolutelly make sense to throw the book at those who are local citizens who have more money than most and yet use it to evade a duty to Society which is likely higher than that of most other people.