A free press also includes a free press for people you disagree with.
But media you don't like being produced at all is perfectly compatible with a free press, including dislike because of influences and pressures you disapprove of. (In some sense, it would be extremely surprising if you liked all the media being produced.)
FWIW I don't think Facebook is likely any better in this area than TikTok, or indeed any social network or platform based around user generated content. It's likely always possible to create popular content that subconsciously influences people's thinking.
One thing that might separate Facebook from TikTok (for some people, not necessarily myself) is the question of "do I trust who is serving this content?" - in these days of algorithmically generated feeds, these companies can likely get away with more in terms of inserting specifically targeted content etc. without it looking suspicious, and have people assume it's showing because it's organically popular.
In regards to the value of 60 second funny videos to share messaging, part of the strength here may be exactly because it's a platform for short, funny videos; as long as the ideas being communicated can be slipped into a funny video in a subtle way, people are hearing them without even realising it. (e.g. perhaps videos making fun of American leaders, undermining their authority etc. - certainly not hard to do with certain leaders...)