I saw this internship posting on LinkedIn:How does the applicant counter work on LinkedIn? I find it hard to believe that 558 were sent in one day. 
How does the applicant counter work on LinkedIn?
linkedin
My assumption is that the counter is highly inaccurate. I did hit the Apply on the company website button once by accident and surprisingly found the counter was incremented on the LinkedIn page, even though I did not proceed with application. I checked this few times later, every time you hit that button (apparently from unique profile) the counter goes up by one, but I do not take that counter seriously anymore