The OP's comment was different. He was using youtube-dl to download videos uploaded by his own clients, which was fine because they're the copyright owners. Transcoding doesn't generally create a separate copyrighted work because at least for these types of media, the underlying representation of the bits doesn't matter.
Note: this isn't fair use. Fair use is a defense to violating copyright, and a copyright owner can't violate their own copyright ...but if they licensed one or more copyrights to a third party, they could violate the third party's copyrights depending on the terms of that license.