Nope not wordfence. I’ll to do the full plugin test after hours and see what happens.
Quick thought. Could it be Wordfence and its firewall?
It shows the IP of the site itself. 162.214.30.28 Below I pasted the latest the entries from the log.
13th Night Curriculum (id:8077)
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http://popcultureclassroom.org/wp-content/uploads/2016/08/13TH-NIGHT_Curriculum_For-Print.pdf 162.214.30.28 2016-09-05 06:41:58 United States Not Logged In
13th Night 8.5 Comic (id:8075)
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http://popcultureclassroom.org/wp-content/uploads/2016/08/13th-NIGHT-COMIC_8.5x11_FOR-PRINT.pdf 162.214.30.28 2016-09-05 03:17:56 United States Not Logged In
13th Night Curriculum (id:8077)
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http://popcultureclassroom.org/wp-content/uploads/2016/08/13TH-NIGHT_Curriculum_For-Print.pdf 162.214.30.28 2016-09-04 15:47:33 United States Not Logged In