My understanding of the legality and propriety of hospital "advertising" in social media was rather vague but an article on this topic cleared away the cobwebs (see: Hospital Advertising). Below is an excerpt from it. It turns out to be legal but later in the post I will discuss why I think it's beneficial for healthcare consumers.
While advertising by doctors and hospitals has been legal for 30 years, until recently, professional taboos discouraged the practice. Increasing economic pressures and changing cultural norms have led, however, to the demise of these informal proscriptions, and advertisements produced by hospitals and individual providers are now common. Yet arguments against healthcare-service advertising can be made on both ethical and economic grounds. While advocates of healthcare service advertising argue that the practice is harmless, often educational, and economically essential, several recent studies of healthcare service advertising reveal that medical centers and individual physicians often create advertisements that: (1) Manipulate patients’ ignorance and vulnerability; [and]...(2) Stimulate demand for unproven or ineffective therapies.
Regarding hospital "advertisements" in social media, I chose at random the topic of transfemoral aortic valve replacement (TAVR) and found some very instructive videos posted by hospitals and explaining the procedure on YouTube (see, for example: TAVR saves bowler with aortic stenosis; Transfemoral Aortic Valve Replacement Animation; Aortic Valve Stenosis and TAVR Overview). The sponsoring health systems for these videos were Northwell Health, Gundersen Health, and University of Texas Health. None of these videos were a hard-sell to promote TAVR by the hospital sponsor but rather, appropriately, an educational tool for helping patients understand their treatment options. I have the feeling that hospitals are ramping up their social media posts about healthcare topics and I think that this will provide broad benefits to consumers.