They most certianly can arrest you for reckless driving...however 20 mph over in a 50 MPH speed zone is not reckless driving unless conditions are horrible...and even then, the cop would probably write you a ticket for driving in a manner which conditions don't permit before a reckless. The ticket has a fine amount on it for 20 MPH over even, it just wouldn't happen, and if it did happen, it would NEVER stick.

And if he walks into the courtroom bragging about how he was going 80, yup, the judge will screw him. If the lawyer tels him to announce his speed to the judge, then the lawyer needs to be shot. More likely, it'll be something like, "Well, I dunno exactly how fast I was going as I wasn't paying constant attention to the speedometer, I might've been speeding by a litte bit, but all I remember is this cop flying up behind me and flipping his lights on then saying he was pacing me doing 90. I'm sure I wasn't doing 90 or anywhere near 90." And they'd take it from there, depending on what I mentioned.