What I understand this to mean is that the editorial staff of these journals rejected the paper.

After the scientist decides to submit a paper for publication to a specific journal, the paper will first reach the editorial staff. The staff will look at the paper and assess whether they want to submit the paper to peer-review. At this stage they can reject the paper for a number of reasons - they may think that the research is not relevant enough to the journal's focus, too narrow or too broad in scope, that it does not meet their quality standards in some metric, etc... This is a first filter.

The editorial staff might have a scientific background but they are generally not experts in the specific field, and so a rejection at this stage does not necessarily reflect the quality of the underlying science which they might not be able to assess. That's where peer-review comes in. If the editorial staff likes the paper, they will submit it to experts that should have experience specifically relevant to the research described in the paper for peer-review. This process consists of a back-and-forth between the authors and experts in the field, with the editorial staff acting as intermediaries. The editors will then take into consideration the back-and-forth between authors and peer-reviewers and they will determine whether to accept or reject the paper.

You can look at an example of the description of this process from Nature here: https://www.nature.com/nature/for-authors/editorial-criteria-and-processes. Nature is an example of a high-impact journal that will usually reject papers if they deem them to be too narrow in scope, not novel enough, or if the paper does not meet a very high standard of quality.

An especially relevant paragraph from this page is the following:

The first stage for a newly submitted Article is that the editorial staff consider whether to send it for peer-review. On submission, the manuscript is assigned to an editor covering the subject area, who seeks informal advice from scientific advisors and editorial colleagues, and who makes this initial decision. The criteria for a paper to be sent for peer-review are that the results seem novel, arresting (illuminating, unexpected or surprising), and that the work described has both immediate and far-reaching implications. The initial judgement is not a reflection on the technical validity of the work described, or on its importance to people in the same field.