It doesn't seem like you're offering "medical advice" by telling them which hospital to go to. If you tell them where to go and they have a bad experience you can always tell them it probably would've been even worse at the other place.
Anyway, I suppose you could say something to a crewmate like "I've always had good luck at Such-and-Such General" within earshot of the coach if you're really paranoid about things. That way he's still making his own decision.
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