Heat came in with the idea of all 3. Sounds like the Bulls had a legit shot, but the Bulls will be Bulls. They were split on doing what was necessary to get all three, they wanted commits from all three, and Rose being absent in recruiting also hurt. Surprisingly, the Bulls were fearful of Wade playing possum, but it seems like Wade went ahead and basically gave the Heat plan away trying to get Chicago to do the same. I had heard that in Wade's first meeting, the feeling of putting on the jersey greatly affected him. This article and his statements since then have all confirmed that much.
The Bulls went last. It was the Saturday afternoon of a holiday weekend, and their group had forgotten to book a car from the hotel. They arrived at the IMG Building in taxis but didn't know to enter through the garage. They were stuck waiting on the street with the door locked.