Publishing without a pre-defined PhD topic? I tend to believe that starting with a well defined goal is an undeniable prerequisite for publishing a quality paper on a certain topic. 

Alas, can a PhD revolve around a fuzzy subject, that offers the student a lot of freedom of choice regarding what problem to solve, as long as the problem is solved using the methods in that field of study?

More explicitly, is it possible to develop a quality research paper in an applied scientific field without fixing the goal beforehand?
Your question contains two related questions


"can a PhD revolve around a fuzzy subject... as long as the problem is solved using the methods in that field of study?"
Is it possible to write and publish a quality paper without a well-defined goal?


In research, almost by definition you do not know what you are going to find. (See the answers to this question.) If you did, it wouldn't be research! So it is definitely possible to have your PhD 'revolve around' a fuzzy subject. But when it comes to writing the actual paper, you will need a well-defined goal for the paper. The paper may not, and probably will not, cover the entire scope of your research. So although your research goal may be nebulous--at least in the beginning--when you are writing a paper to report the findings of said research, you should be able to very clearly articulate  the purpose of this specific paper.