It does a disservice to the health ministry to invariably pin it as “Hamas-run” like the media usually does. It’s a professional, bureaucratic apparatus. Not really any more Hamas-run than the US Bureau of Land Management is Democrat-run. Which is to say, technically accurate but usually stated with a purposeful insinuation.
All this is to say that you’re right, they’re concerned with accuracy and credibility. But credit where credit is due, it’s because of the health ministry itself, not Hamas.