Here's the deal: From 0-~30MPH, the car (a P85D) is limited by friction grip on the road. Note that they have decent size wide tires as a stock item, and the car weighs about 4700 lbs, so the grip is pretty solid. You *WILL* feel the slightest road imperfection- gravel, potholes, water, anything that causes any slip on a high acceleration "launch". The car does a great job of recovering and keeping the other wheels moving you forward (rather than careening into a ditch).
The existing 3.05s time has been verified many times over. (3.2s is for the original models; there was a software upgrade to take off 1.5 s).
Above 30, the car is software limited to save the hardware- it can't dissipate heat safely enough to keep up the max current draw that opening it up all the way would do. What this update does is replace the contactors and safety hardware to allow a higher draw so that the car can keep the limit very close to frictional limit all the way up to 60 without burning up any of the electric drivetrain. (400V/1200A -> 1500A)
Although I have not seen the 2.8s 0-60, I assure you the performance is real. It is an incredible piece of engineering. (source:I own a P85D). Search Y/T for videos of "P85D insane mode" and watch the dashcam to see people's reactions- unless you are a fighter pilot or something, it is a feeling like nothing else.
Also note that since the car is silent, you can often launch right in front of a cop while he eats his doughnut, and if you lay off the throttle by the time you hit the speed limit the radar gun won't catch how fast you accelerated.