IMO the idf and Israeli gov social media is beyond unprofessional, they say stuff that is just wrong accidentally all the time on top of propaganda. It’s pretty clearly run by some people with very extreme views, and very little care for the weight of their tweets.
A few hundred metres is “just behind” when it comes to these rockets and missiles, they travel a long way with the initial stage so that if there’s a misfire, they don’t kill the people launching them. So that seems fine.
If anything hospital being told to evacuate and the international furore and backlash over that demand makes it less likely to be Israel because it’s terrible PR.
I’m not saying anything is for certain, I just think the balance of evidence is tipping one way.