Figure out what was going on, very obviously. Failing that, be open to observing longer instead of kicking him back out when he was still showing obvious symptoms.

His point in talking about being woken up all night was not that he didn't want to be tested, it was why would you even kick someone out onto the street at the crack of dawn who you know hasn't slept all night because you kept waking them up, let alone doing that if they're also sick? (I know the answer, not enough beds, but your "I don't see a problem here" attitude really doesn't contribute to anything.)