We shouldn't put peer reviewed studies on a pedestal. The replication crisis unfolding in biomedical research, neuroscience, psychology, and other fields is largely about researchers trying to game the peer review system. At the same time, researchers in physics, biology, and social science frequently post working drafts on preprint sites, such as http://arXiv.org, http://biorXiv.org, and http://SSRN.com. Some of these sites are event experimenting with postpublication review, where reviewers post comments and recommend changes after the paper has gone public. (More here: http://www.the-scientist.com/?articles.view/articleNo/37969/title/Post-Publication-Peer-Review-Mainstreamed/)
In general, "researchers at university X found that ..." is going to overstate things, unless the "..." is about the particular observations that were made: "researchers at university X found that 7 of 13 participants preferred chocolate with peanut butter instead of jelly." Generalizations should be supported by several studies, preferably done by different groups of researchers over a period of time.
I would recommend that journalists emphasize methods and context rather than findings. In other words, first, science journalists should help readers understand how a study was done. Was this an experiment, a field study, or based on historical data? What techniques were used to produce the data, and how were the data analyzed? What assumptions did the study rely on? What limitations did it have?
Second, science journalists should help readers understand the scientific and social significance of the study. What other research has been done in the area? Does this study conflict or agree with that research? What disagreements do researchers in the field have? What arguments do they give for their views? Does the study have immediate commercial, policy, clinical, or social implications, or are the implications of the research more vague or long-term? (Very little "cancer research" is designed to directly produce new treatments.) If the research is socially controversial, what other factors ("besides the science") are contributing to the controversy?