There can be liability. 15 USC 52 says that "It shall be unlawful for any person, partnership, or corporation to disseminate, or cause to be disseminated, any false advertisement". In the case Standard Oil v. FTC, 577 F.2d 653, one of the petitioners was Batten, Barton, Durstine Osborn, an advertising agency. In this particular case, using a set of tests established by previous case law, the court find that "BBDO knew or should have known of the deceptive nature of the F-310 advertising". See p. 13ff of this FTC document regarding advertising agency liability, which summarizes the situation that
An ad agency does not have to substantiate independently the claims or
scientifically reexamine the advertiser’s substantiation. However, it
cannot ignore obvious shortcomings or facial flaws in an advertiser’s
substantiation.
Cases also include catalog marketers, infomercial producers and even Home Shopping Network. Given the right knowledge, a broadcaster could therefore be liable, if they know they are broadcasting false advertising.