Then the seller can file a DMCA notice, and your video (and maybe your website, too?) would be taken down. If you’re going to use it for commercial purposes, please be honest and pay for it.
No, there’s no written document. Save the screenshots of the bought (and completed and paid for) order, that’s your proof that you have paid for the commercial license.
Edited to add: in addition to the above, using a VO or anything you purchase here for a commercial purpose, but without paying for the commercial use, is a violation of Fiverr’s Terms of Service.