Except this isn't just a "narrative" being pushed by Time; YouTube explicitly wants the power to curate and actively uses that power in their business model: they curate ("recommend") videos to optimize engagement. If they want to wield editorial power, they are need to be held responsible for the consequences of their exercise of that power.
The traditional way to avoid this problem is to make the platform into a common carrier that explicitly and visibly segregates itself away from anything that might be seen as using editorial power. The post office isn't held responsible for someone mailing a threatening letter because they just delivered the (sealed) letter and couldn't know anything about the content.
> direct competitors
Yes, as a publication that can be held responsible for their editorial decisions, Time would like YouTube to be held to the same standard.
Plenty can be said about bad social influences of modern quackery and different types of anti- movements.
An interesting topic is that since they ban some positive everyday-life things, to what extent should they (as perceived by the audience) have a burden of impartiality in the spirit of free discourse in the open society?