Does a research group actually review every applicant's documents in case of overwhelming number of applications? It's like the response to my PhD application usually includes something like "The number of the applications we've received is so high that we can't accommodate all of the qualified applicants." It's like outnumbering applicants is the general reason of rejection. 

Besides that, they seldom address other reasons. Some responses of this kind were due to my enquiry after application, rather than on their own initiative. Some of them didn't bother to respond even after my enquiry. 

So I wonder whether a research group or school actually reviews every applicant's documents if they receive an overwhelming number of applications compared to the vacancy number. Maybe they have a way to pick some among the large number of applications — like using the filter function of a computer to pick documents containing some kind of keywords, which may not be completely faithful — to actually review to consider who to admit and that's why they don't bother to reply to all the applicants they don't admit.

For example, recently I found the reason I was not admitted for an application to a fundamental physics research group in Europe four months ago is eventually the funding is only available for a research project which is not my research interest; thus probably they even didn't review my application as they, saying they received an extraordinary number of applications, only picked those whose research interests involve that research project to review.
When I get applications to review, I usually do a pre-pass on every application. I look for GPA, test scores, and compliance with requested application materials (i.e. did they even have anyone write them letters of recommendation?). We usually have explicitly stated bottom line cutoffs for GPA and test scores. Those falling below these marks are automatically set to the side. 

I next try to scan the research statements / statements of purpose. This eliminates a large amount of the candidates usually. 

I then cut the remaining applications into about half. I select who I want to accept from this half stack and order them roughly from strongest to weakest. I then do a spot check to see if anyone in the other half stack is clearly superior to the weaker candidates in the already selected stack. If so, I do an insertion of the new candidate and the weakest person is dropped from the list. 

In the end, yes, I've looked at everyone's application, and no, I have not given heartfelt and deep thought to each applicant. 

We then send out an accept/reject form email to every applicant. I very rarely even reply at length to students who fight their rejection.