Oh, they get special treatment. But you're not going to find a smoking gun. There's no memo. But, these teams do know what's being tech'd Miami weekend and what's not. In other words they'll know where they can push it and where they can't. They will be given benefits of the doubt, etc. I remember when the 78 first made it to the Final Four and went through inspection, they passed it, but the inspection tech told the team president "you're going to need to push it MUCH further than this if you want to have a chance." They thought they were being set up. They weren't. They got creamed that race. But, they also learned how to "play the game."
Aside from minor tech advantages there are also other things to consider. No other competitor out there is going to race them hard. No one wants to be the guy who wrecks a contender. Plus, every single ounce of intelligence within a racing organization is solely focused on the championship 4 car. So, aside from the top car getting even faster with additional resources, the other standard front runners from within those same organizations might be lacking since they've had the "B" team on their Homestead car.
But still, even with a slight tech advantage (and it is very slight, it's not some outrageous advantage that anyone can walk by and spot) you still need to race a clean race, and have decent speed going in. NASCAR could give a 15th place car the same advantage and they'd still be lucky to crack the top 10. But when you have a top 3-8 car already, a slight edge (along with those other variables) would be enough to ride up front most of the day. Tech might also help you qualify better, and this is definitely a track position type race.