I really don't know any "bad" teachers. It's sort of hard being a bad teacher, in the way you guys are implying.
To me, a "bad" teacher is one who either does not care about his students, or doesn't know how to teach in an effective manner.
However, very few teachers will actually teach you how to play incorrectly. At most, they will not teach you how to play correctly.
So I think getting a "bad" teacher is not really a problem. Furthermore, piano isn't really something that differs from the norm. So if a teacher gives real bad and incorrect advice, I think the student should be able to figure it out (given that it's not a young child).
In the end, I think a teacher is most important in introducing concepts. For example, you can't learn calculus if you never knew such a thing existed. Only when you know that it exists, can you try to learn and master it.
Similarly, there are many aspects of piano playing that are not easy to figure out on one's own. For example, tension, muddy pedaling, rubato, legato... and many more. The most difficult step is to go from ignorant to knowing that these things exist. Only when you know they exist can you start working on improving them.
And it's hard to realize that these factors exist without a teacher.
So I think stevebob's point on whether a person's had lessons but is currently not having lessons versus a person who's never had lessons is a good point.
The former, possibly. The latter, highly unlikely.