In January a group of self-declared "sceptics" hit the headlines with an attention-grabbing publicity stunt. If you instinctively interpret that sentence as a reference to the battle-scarred topic of climate change, then it is a mark of how successfully those opposed to the scientific consensus on climate change have appropriated the term sceptic".

In fact, the event in question is the mass homeopathy "overdose" staged by the Merseyside Skeptics. Do the Merseyside Skeptics (and hundreds of other groups like them) share much common ground with the army of Freedom of Information requesters currently swarming around climate science databases? Or could it be that climate change sceptics are giving wider scepticism a bad name?

Over the past three months climate change scepticism seems to have reached new levels. The Guardian's investigation into the emails hacked from the University of East Anglia has shone a rather uncomfortable light into the sock-drawer of science. But it has revealed nothing that challenges the fact that the climate is changing – or that human activity is responsible. Trust has been diminished, embarrassing exchanges have been revealed, but the clunking wheels of the anti-climate change lobby have gone into overdrive, falsely claiming that the case for human-caused climate change has been discredited.

Climate change sceptics often position themselves as the antidote to the hysterical, exaggerated claims of climate scientists and environmentalists, adopting the tools and language of "rational enquiry". But something is missing from this picture - where are the voices of the truly sceptical thinkers that the climate sceptics claim to represent?

The website of the long-running US magazine Skeptic describes scepticism as a method rather than a position, and one that is embodied in the scientific method. A search of the magazine's online archives reveals not one article disputing the science of climate change. However, there are several debunking unsubstantiated claims that climate change sceptics have made. The not-for-profit organisation UK Skeptics is even less welcoming to climate sceptics, with a helpful note stating:

We are nothing to do with opposition, activist, or denialist groups who wrongly refer to themselves as 'skeptics' because they adopt a position of non-belief (eg global warming skeptics, vaccine skeptics, etc).

The distinction between scepticism and non-belief is a crucial one. While scepticism is healthy, non-belief in the face of overwhelming evidence is the antipathy of scepticism. Recent climate scepticism has been characterised by a visceral mistrust of science, scientific institutions and scientific governance. Never mind that the case for climate change has been painstakingly pieced together over decades – climate change sceptics are busy writing it off on the basis of a few inconsistencies.

But embarrassingly for climate change sceptics, the people who have thought longest and hardest about what it means to be a truly sceptical thinker seem in a hurry to distance themselves from their fellow sceptics. Michael Marshall, from the Merseyside Skeptics group that organised the homeopathy overdose is clear about the legitimacy of climate change sceptics: "In our view, climate change sceptics are not sceptics. A sceptic looks at the available evidence and makes a decision, and for homeopathy the evidence is that it doesn't work. But the sceptical position on climate change is that it is happening."

John Jackson, from UK Skeptics, agreed, added: "Terms like "climate change sceptic" are very damaging to scepticism - basically because this is not what scepticism is. We often get people calling us, referring to themselves as climate sceptics, but we argue with them. We accept global warming because the evidence is overwhelming."

With trust in climate change and climate science rapidly dwindling, statements such as these could become incredibly powerful. Here are groups of intelligent, rational, scientifically literate, independent and sceptical thinkers, directly contradicting the view of the so-called climate sceptics. Debate continues about whether "denier" is an appropriate term for those who oppose the climate science consensus. But it seems clear that "sceptic" is no better – the sceptics themselves reject the climate contrarians' claim to their title.

Along with preachy eco-warriors and morally bankrupt politicians, climate scientists are in danger of being added to the list of sources that aren't trusted to communicate climate change. Perhaps it is time for the silent army of rational thinkers to stand up for the science. They could be the one authoritative group that could argue the climate change case – and all from a position of scepticism.

• Adam Corner is a research associate at Cardiff University. His interests include the psychology of communicating climate change