The "view close votes" privilege implies, through its name and page text, that you can see all close votes:
How do I view close votes and reasons?
Click on the "close" link under any question body. You may also cast a close or reopen vote on your own question.
However, that's not true. At this level, you can only see close votes on your questions, because the actual ability is "Vote to close, reopen, or migrate your questions".
This is either a bug in the privilege name & page, or it is a bug that the close reasons aren't displayed on other questions. Going by historical behavior, I'd say the privilege page is the bug and it was a slight oversight when creating the privileges en masse.
I've updated that page to be explicit, but the privilege name is still misleading, though that's a much smaller issue cleared up by actually reading the page. My understanding is community edits to privilege pages don't immediately take effect, so for now you can only see the edit in the history.