So yeah I can see why you choose not to take their word when they say that they have evidence.
But trust me bro :-)
But seriously now, I don't really understand why it would be shocking to discover Hamas is operating from hospitals, mosques and schools. They are fighting a war and will do anything they can to gain an advantage.
It's very convenient to deploy your base under a hospital, for so many seasons, that I really don't understand why people find it hard to believe...
I don't think you're wrong, but I think its wrong when the response is "lets bomb them" instead of figuring out something else.
You could send troops in, but now you're in disadvantaged close quarters combat, which is horrific and guaranteed to get many of your troops killed.
The only reasonable strategy is to bomb the hospital. It saves the loves of your troops. Will there be civilian casualties? Yes. Is that preferred to losing your own citizens? Absolutely.