The CC NC clause is really hard to get a grasp on, and Creative Commons do not provide much guidance about it.
There certainly exists a lot of examples where it is not possible to give a straightforward about exactly what is commercial use. For an example of such a situation, see my answer to this question: Using CC-NC material inside a freemium app.
That being said, I don't see why there is a need to cop out of every question about the NC clause by simply saying that it isn't clear.
Sometimes it possible to give a straightforward answer. Then we should.
AFAIK, there is almost no case law about the NC clause. This means that it isn't often contested. In most cases, people are able to figure out if it applies or not, and do the right thing.
This question is one where I think it is reasonable to provide a straight answer.
The legal code defines "Non-Commercial" as:
not primarily intended for or directed towards commercial advantage or monetary compensation
That means that you cannot sell it for an amount of money that will make you a profit.
As for someone asking you to print a model, you can obviously get compensated for your direct outlay in materials, but if you make a profit by providing this service, you're breaking the license.
Until October 2008, the CC FAQ provided a much more detailed guidance on how to understand the "NC" clause than the present, deliberately vague FAQ, does.
The old FAQ discussed a scenario where a commercial print copy shop were charging the commercial rate for the service of making copies of some materials licensed under CC BY-NC, and concluded that this was not allowed. However, if a commercial print shop agreed to just charging its own costs for the same operation, then it would be OK.
While this specific example has since been removed from the CC FAQ, I think it still applies.
As for the owner allowing you to sell it: Yes. CC is not an exclusive license. As with all CC licenses, can always ask copyright owners for an alternative licensing arrangement.