Hi,
Each item/creation is subject to its' own license and you need to make sure that the license permits you to use whatever you purchased for commercial use and/or that the intellectual property rights/ownership rights have been transferred to you, or that you've received a license to use the item/creation.
In regards to Fiver - the section you mentioned does mean that the person doing the gig is assigning the rights over to you - the only problem is that that person may not be the owner of those rights, meaning that he can't actually assign them to you. For example, if the Fiverr person did something for someone else (and already assigned it to them), and then uses those same materials for you...
Good luck
I've successfully helped over 350 entrepreneurs, startups and businesses, and I would be happy to help you. After scheduling a call, please send me some background information so that I can prepare in advance - thus giving you maximum value for your money. Take a look at the great reviews I’ve received: https://clarity.fm/assafben-david