My hobby is genealogy and I'm quite passionate about ensuring that I only use confirmed evidence; because of this I've become a very experienced researcher, but even I get caught out from time to time.
My point is that most people are not researchers and have been brought up to expect and believe that matters in the public domain that are repeated by politicians and 'quality' newspapers, in this case the Telegraph, have been duly researched before publication. Historically we have, in the main, been able to believe what newspapers print - there's been an understanding that our libel laws will protect the veracity of news stories. And although politicians now have a reputation for 'all' being liars the truth is that I expect the majority are a hardworking, trustworthy bunch of people who are incensed to have their integrity trashed by the few who are not. People can hardly be blamed for still being trusting when the change in political veracity has been so sudden.
News stories now are fast moving and journalists and some politicians and journalists are prepared to get into print without checking the facts first. I think when the story in question fits their agenda this is often done deliberately. (I am NOT talking here about any one newspaper or political party).
Not everybody has the time, the will or the skill to research every possibly 'dodgy' story, so websites like FullFact, FactCheck and the BBCs Reality Check have sprung up to make the task of discerning facts easier. This is why there was such dismay when the conservatives pulled their trick of dressing up their website to look like a bona fide fact checking site.