I think there would be no issue with it if he had not used trademark names and logos. API calls to youtube, pulling up a channel, playing videos... if Youtube/Google doesn't have a policy like Apple to not allow apps that duplicate their apps functionality, I don't see how it could be a problem. Most probably is that problem arose with trademark infringement. This is a serious issue since 3rd party using your trademark without authorization can tarnish your carefully crafted design/brand experience as well as confuse customers.