Yes, those requests are coming from FullStory's servers. We snapshot your public static resources for you automatically alongside recordings so that you can be free to change your website at will with the ability to play back older sessions as they were at the time they were recorded. This is great for before/after analysis.
Also, to be clear, we only request each unique resource once across any recordings that use it. (And we throttle and cache aggressively on our side to make sure we don't add anything above negligible load on your servers.) So, it would be normal to see relatively more when you first deploy FullStory and then they'll taper off significantly as subsequent recordings refer to the same set of URLs for your static resources.