There are 2 things to take into account
One, Apple did indeed do a dirty by disallowing that app but allowing a very similar app from a group of hospital employees.
Hospital employees are generally not programmers. I would have more trust in an app made by actual programmers. In this case, of course, said programmers would have had to have some oversight in privacy protection measures and maybe medical counsel as well. I did not see that that was specified.
Two, a claim filed by an apparently non-existing "company" who does not identify a single person in the company, doe snot come forward with the list of its employees, partners or collaborators who worked on the app, and can apparently only be reached by calling the CEO of another company is not exactly a brilliant confidence generator.
So, as much as I'd like to harp on Apple for once again changing the rules after the fact to suit itself, the shady side of the complainant makes me side with Apple.
If you're honest, you're not supposed to hide stuff when filing a complaint in court.