In my (former researcher who left to industry) opinion/experience its not the editors who put the pressure, but the possibility that you ignored a work of somebody who is important enough to referee for Nature or Science. There are some components of these phenomena:
a) Maybe the work really is important, and you did not know it because it's too long ago. There is usually nothing wrong with a referee saying "hey that is similar to what [xyz]" did, even if they are on the list of authors on the reference in question.
b) some referees dont react positively to not getting cited and will shoot down any paper not referring to *their* theory for other reasons (i believe that happened to me once)
c) In the abstract (which is the part really read by the editors before the refereeing process) you compare your paper to the previous publications. Authors are under the impression that comparing your work to previous important papers makes a better impression. How far this is true i cant judge. I found the editor stage *before* the refereeing in Nature and Science the most intransparent thing I have experienced as an author. Unlike the refereeing process there is no way to appeal, there is not information on what the editors disliked so much to refuse directly. (There is the saying that once you had Nature/Science papers it gets more likely to pass this stage, and i have seen at least one example of a paper being passed to Nature which for sure would have been rejected by the editors had it come from a less important group in the field)