The second Steve heard the house was open and people were out he left the police station for the hospital. He got a run down on the injured, how the medical staff was holding up and then names.
He probably didn't look like a concerned friend marching through the halls of the hospital like he was at SHIELD on his way for a debrief but it kept people from bothering him. His teammate was out but injured and after he got a read on how well Clint was, he'd get a rundown on what went on inside that house.
Apparently, things were worse than he thought because he spotted Clint trying to make a break for it with a bottle of booze in hand. Judgment could wait.
"Should've known you'd try this," he said as he approached. "Can't stay still in my world either. Did you get cleared to leave?"
He looked him over and was a little skeptical of that. Clint did not look good. He looked like he was in pain.