This is not correct. Section 230 does not restrict or amend a sites freedom of speech, nor does it make a distinction between a platform or publisher.

The effect of the law is that sites have less civil liability for user generated content, even if they make some decisions about what content is acceptable.

Those decisions can't get limited under the first amendment, and the content still has 3rd party speech protection.

So the government asking YouTube to remove a video would be a 1a violation, by controlling it's moderation decisions.