How to take the endorsement request for arXiv?
First of all


  The mail to me was also cc-ed to some big persons in top-ranked universities.


For me this would already be a red flag and result in not endorsing them. The Arχiv explicitly instructs you not to spam when seeking endorsement:


  Please note, however, that it is inappropriate to email large numbers of potential endorsers at once, or to repeatedly email the same endorser with a request for endorsement. 


Endorsing somebody you do not know

Endorsing somebody you do not know is somewhat equivalent to saying that the article would pass the initial check of some (reputable) journal, i.e., with endorsing you confirm:


That the article adheres to basic standards of scientific writing.
The article is not complete bogus (e.g. neglecting well-established facts).


From the Arχiv’s help pages:


  We don't expect you to read the paper in detail, or verify that the work is correct, but you should check that the paper is appropriate for the subject area. You should not endorse the author if the author is unfamiliar with the basic facts of the field, or if the work is entirely disconnected with current work in the area.


Endorsing somebody you know


  Is it somewhat based on the hypothesis that if you know a person A and you have already published in arXiv before, then the work of A is also publishable in arXiv.


Not exactly; it is based on the assumption that if you have published on the Arχiv and know person A, you are qualified to judge whether person A is likely to attempt to publish sub-standard content on the Arχiv. If you know person A and also know that person A is not remotely capable of proper scientific writing (and research), you should not endorse them. For example, you should probably not endorse the ghost-healer who happens to live next to you.

Explicitly not endorsing somebody

It may be helpful to explicitly not endorse (instead of doing nothing) if you think that somebody should not be allowed to publish on the Arχiv. Otherwise some sloppy endorser may unilaterally allow them to do so.

If you do not want to endorse somebody, you have to select either “I do know […] personally” or “I have read the paper […] intends to submit” (at least this was the case half a year ago), even if neither applies and you refuse endorsement due to them spamming their endorsement request, publishing in predatory journals, or similar. (This was confirmed to me by the Arχiv when I had this problem.)