Just to check one file that would not open, a pdf, was still available online so I downloaded that file and it opened just fine. I compared the 2 pdf files and their sizes are exactly the same 217313 bytes. If it's corrupted it seems that the file size ought to be a little different.
If you try to move the newly d/l'ed PDF to the same location as the old one do you get an "already exists" pop-up? And if you do and then hit "Replace", what happens? (Make a command-D copy of the original before trying.)
One of the pdf files which was a legal document now shows a picture of my dog when opened. Very weird.
Have you interrogated your dog?