IMHO, twitter links come from the mouths of actual people, rather than news stories. So I think tweets are more "accurate" then a journalistic article from an online newspaper, where you might get quotes but largely it's the journalist who's interpreted it and written around it.
The root cause, if you can call it that, is not where the link is derived from, but it's the way in which people use links to validate their opinion. I have noticed that people tend to give more credence to a tweet than they do from a DM link. But we are all free to do that from whichever source we choose. So if you ban one form of quoting/linking then you'd need to ban them all.
Nothing is stopping anyone from replying to a quoted Tweet and saying "I don't agree with that".
