Re: "no way to account for every possibility"
Yes there is, with clearly delineated types, values and branches.
As the software engineer, it's your job to control the data and create the pathway it takes. If you can't control that process then you haven't created it properly in the first place. You don't need to blacklist an infinite pool of invalid possibilities, you only need to whitelist the valid ones.
The problem is not that software is "impossible to test", it's just that software is increasingly being written by people who are not applying basic engineering principles to the process, using tools that designed primarily for monkeys to make money, not engineers to solve problems.
The statement should be amended to "badly written software is difficult to test", but as it stands it's pure bullshit, just an excuse for sloppy programming.