How detailed are you supposed to be w.r.t. your research interests in a SoP?
I do not think you can be too specific about your research interests.
You said

not offered admission because how they explain their plans of research are &quot;too specific&quot;

What has actually happened here is that the applicant has applied to the wrong university.  You should follow these steps:

Identify faculty working in your area of interest.
Contact them and ask them if they are recruiting PhD students in that area (if it is not already stated publicly).
Apply, stating in your application that you wish to work in an area (or a few areas) where you know they are recruiting.

Then your application will never be &quot;too specific&quot;.
If your research interests are not specific enough, this might imply you do not know what is involved in a PhD and you might not succeed as a PhD student.