I would not say that shorts are not welcome. You might get some looks, but I have seen people in white T-shirts, shorts and flip-flops (yes, that is exactly what I said.) Any others want to chime in?
Dress was casual. I like to wear long pants to dinner but I really seem to be in the minority on this one, especially downtown! Eat at Binions a few weeks ago and half the crowd was in shorts.
Haven't been to Binion's, but the Flame was fantastic Monday night. They are 2/2 with me. Highly recommended. Shorts/t-shirts are fine, at least in summer.