Without a high level of intelligence, he wouldn't be able to effectively sell out. There's timing involved that takes read and recognizing what's coming at you, which requires "hockey sense." Playing a positionally sound game is a result of intelligence too.
I think you are overstating this honestly. It sounds like you are describing him reading a pass and then exploding out of his skates to intercept a cross ice pass or something. Defenseman who do that are what I think of when I think hockey IQ. Reading and breaking up cross ice passes, drop passes along the boards. Girardi's game never entailed this. Also due to his average size and mobility. Lacks the reach and the speed to be able to do stuff like that a lot.
When I look at Girardi's body of work over the years, I just don't agree that his game was a result of above average or great 'hockey IQ'.
While he saw success in his game, I still stand by it was the result of selling out and diving/flopping like a fish on the ice to do whatever he had to do to try and keep the puck out of the net.
Another big issue with Girardi is alot of all of these blocked shots he accumulated over his career were because of himself. Very average puck mover at best in his prime, and him not being able to get the puck out of the zone at times are why he had to block so many damn shots.
I am usually on Girardi's side when this thread blows up. I still see him as an asset. I believe his very underwhelming advnaced stats are partly the result of playing a very nuanced/niche game which entails the accumulation of Corsi Against at the expense of lowering shots/chance quality, but there's no denying he also put himself in harms way too and some of the severity of his numbers are certainly his fault.