You can't show a program to bug free. You can't prove a negative.
"the last three versions of the program -- each 420,000 lines long-had just one error each. The last 11 versions of this software had a total of 17 errors."
Translation: in each of the last three versions, only one error was found, in the last 11 versions, only 17 errors were found.
"the shuttle group now finds 85% of its errors before formal testing begins, and 99.9% before the program is delivered"
In order to know you've found x% of the errors in a program, don't you have to have already found 100% of them? If I find 9 errors in a program, how can I know that I've found 90% of the errors unless I also know that there are 10 errors in it?
A lot of what the author says sounds impressive, but I'd argue a lot of it is either wrong or not even wrong (http://en.wikipedia.org/wiki/Not_even_wrong). Even granting the author some artistic license, he's going pretty overboard in a lot of his claims.
I'm sure the software produced by this group is less error-prone than your typical desktop or web app, but it doesn't sound like they're writing innovative software either. Most of what they do sounds like either mathematical calculations or driving hardware devices. Both areas which seem to me to be pretty well explored at this stage.