Preview fails to open pdf with "The file couldn't be opened because you don't have permissions to view it". but I have these permissions
This is apparently a common problem, and one that Apple's support article below often does not fix.  It also occurs trying to save a new file.  

The work-around both for an existing file that Preview wouldn't itself open, as well as for a new it says it can't save [which it actually already has saved], is this: navigate to the file in Finder and open via Cmd-O.  Then, back in Preview, click 'Cancel' and it will then proceed as if nothing strange occurred.  

It's Apple's version of SNL's Rosanna Rosannadanna's 'Nevermind...' 

This thread. suggests it's a permissions problem, and the referenced Apple Support page gives directions to apply permissions to the user folder via Get Info, then reset permissions in Terminal.

Immediately after I did this, Preview would save a screenshot, but shortly thereafter the same problem recurred.  It doesn't always do it.

My feedback to Apple when the 'fix' did not work was to point out that they just deflected the question.  I asked they address what to do when it didn't work.

It might be one of hundreds of OS issues Apple doesn't know how to fix.   Move on - install Mojave and hope it goes away?