Certainly, people who use the term "conspiracy" in the context you mention are doing it wrong. I would say that the phrase "conspiracy theory" as used in popular culture has a slightly different (and more negative) connotation than the two words alone would lead you to believe. In my opinion, a "conspiracy theory" is something for which serious or even incredible claims are made for which there is little or only circumstantial evidence. Of course, sometimes people are quick to use the term without knowing what evidence actually exists.

I tend to be a skeptic. If someone makes serious claims I expect serious evidence. Conspiracy theories, as I identify them, are often rampant with speculation and light on hard facts. But there are many different kinds and some are more serious than others. At the end of the day, it isn't up to the skeptic to prove a negative, it's up to the conspiracy theorist to provide the proof of what they are claiming.