After further investigating, it seems that the requests are simply blocking .json and certain other file extentions from being requested. .txt files work perfectly fine with AJAX. I guess if I hosted my own website it might work with .json files, but it may actually be a security feature in browsers to protect users, rather than the website itself, but I'm not sure about that.
Basically, don't use AJAX to request .json if you plan on hosting your game as HTML on a site you don't run. Use .txt instead, if you can.