He really is. Even random thugs know not to mess with Harley. In one of the previous issue, some robber guy saw Harley walking down the street and mentioned how hot she was, and the guy he was with told him not to even think about it cause she's The Joker's girl. He then proceeded to tell a story of how some guy whistled at Harley once and they later found him hanging from a drainpipe with his lips cut off. Yep.
But then again, Hush seems cocky enough to think he can handle Joker. Which is why he's stupid.