It is hard to fathom isn't it?
However, let me have a guess or two. I'll order them in what I consider to be increasing likelyhood.
1) The have absolutely no idea of what they are doing. They don't understand polling at all and think that if "my mother says..." then all mothers must say the same thing. So a tiny sample size is not a problem to them since they don't know that "sample size" means.
2)Those conducting the poll do know a bit. But they went to effort and expense and tried to salvage what they could out of it. Sometimes we get caught up in what we are doing and don't realize we should stop.
3) They don't care about the accuracy. They don't care what any knowledgable people say. They have what they want. They will quite officialy refering to the study but it is now out there and will be referred to all over the place. It will become part of the folklore. They aren't willing to be so very dishonest as to make claims without any study at all but they are dishonest enough to alloow the spread of this even though they know full well the results are meaningless.