I'm sorry, but this is a completely wrong-headed statement. Standardized testing for school children and A/B testing for web site visitors are completely different beyond the fact that both involve the word "test".
When you run A/B tests on a web site you don't tell the visitors which version they are being shown, or even that there are multiple versions at all. That would completely destroy the value of the testing. In psychology research, where ethics generally dictates that the subjects be informed, they are still not told what specifically is being tested, lest they modify their behavior.
On the other hand, everyone involved in school standardized tests knows about the tests, knows about various biases that exist within the tests, and knows what is at stake based on the results of the tests.
The reason that the current form of standardized testing is destructive is pure economics. If I tell you that I will count how many lines of code you have committed to the repository at the end of each week and that your pay will be based on this figure, what are you and your coworkers going to do? You're going to start writing hundreds of lines of comments, putting each variable declaration on its own line, needlessly re-factoring satisfactory code, etc. This is, as I understand it, a well-documented side-effect of measuring programmer productivity using LoC.
Once I implement this evaluation scheme, two things happen. First, you are being evaluated based on an objective metric. Second, you have direct control over the value that metric takes on. Economics, which is, to a great extent, the study of incentives, tells us that you (and your coworkers, at least in general) will game the daylights out of the metric.
So why is it any different when teachers, once told that their salaries and very jobs depend on the results of an annual test, teach their students exactly what is on the test, by hook or by crook, even at the expense of "real" learning?
The problem is that teachers aren't oblivious (neither are programmers). When they see that they are being evaluated based on the outcome of X, they seek to maximize X. So the trick is, if you insist on quantitative metrics (which is not totally unreasonable, at least as the default) then the metrics must be linked to the behaviors that are desirable, not some vague indicator that approximately tracks those behaviors.
Edit: missing word