Don't Americans also have rules about hidden advertising like that in regular media?

The American model prefers "sponsored material should be identified as such" though that's only active for broadcasting currently

American law generally favors freedom of expression.

There are several classes of restrictions on free speech in the US. These include: obscenity, fraud, speech integral to illegal conduct, speech that incites imminent lawless action, speech that violates intellectual property law, true threats, false statements of fact, and —- most relevant here -— commercial speech such as advertising.

Advertising has far less protection than is ordinarily afforded to the kind of speech you might do as a person.

You're talking about the country that live-censor speech with beep when people curse on TV…