Oliver uses comedic license when calling him on it:

The target is not the American people. But it seems that too often, you miss the target, and you hit the American person standing next to them going, "Whoa!"

Actually, it's even worse than that. It's as if the NSA identifies its target, throws a net over him, and that net also happens to snag millions of innocent Americans. But they weren't the target!

Alexander replies:

But you see, we're not just out there gathering U.S. communications, listening to their phone calls, or collecting their emails. But that's the first thing that people jump to.

Let's go to the New York Times:

The N.S.A. is not just intercepting the communications of Americans who are in direct contact with foreigners targeted overseas, a practice that government officials have openly acknowledged. It is also casting a far wider net for people who cite information linked to those foreigners, like a little used e-mail address, according to a senior intelligence official. While it has long been known that the agency conducts extensive computer searches of data it vacuums up overseas, that it is systematically searching—without warrants—through the contents of Americans’ communications that cross the border reveals more about the scale of its secret operations.

And The Guardian:

... the intelligence agencies acknowledge that purely domestic communications can also be inadvertently swept into its databases. That process is known as "incidental collection" in surveillance parlance.

Later on in the interview, this exchange occurs:

Oliver: How much information do you need to keep Americans safe? Alexander: That is a tough question. I don't know the answer to that. Here's what I do know. Look at the last 12 years, 13 years since 9/11. We've had a tremendous and remarkable record. That wasn't by accident.

We could also look at terrorist attacks in the United States between 1789 and 1989, long before the NSA had the capability to monitor so much of our private communications. That seemed to work out okay too.

Here's one last exchange that cries out for scrutiny, and really illustrates how smoothly deceptive Alexander is when he speaks:

Oliver: In your mind, has the NSA ever done something illegal? Alexander: In my time, no. Not that I know of. You know, one of the most impressive things that I've seen in my career is people who've made a mistake, that could be a huge mistake, stepping up to say, I made a mistake. And in every case, to my knowledge, everyone except for 12 individuals stepped forward at the time they made those mistakes. Oliver: But you can't say everyone, except for twelve. That's like saying I've never killed anyone, except those three people I've got buried under my patio at home.

A truthful answer to "has the NSA ever done something illegal?" is yes, repeatedly. Alexander seems to think acknowledging illegal spying makes it okay. But of course the incidents he's discussing are just the beginning of NSA lawbreaking. Again, here's the Times (emphasis added):

A federal judge sharply rebuked the National Security Agency in 2011 for repeatedly misleading the court that oversees its surveillance on domestic soil, including a program that is collecting tens of thousands of domestic e-mails and other Internet communications of Americans each year, according to a secret ruling made public on Wednesday. The 85-page ruling by Judge John D. Bates, then serving as chief judge on the Foreign Intelligence Surveillance Court, involved an N.S.A. program that systematically searches the contents of Americans’ international Internet communications, without a warrant, in a hunt for discussions about foreigners who have been targeted for surveillance. The Justice Department had told Judge Bates that N.S.A. officials had discovered that the program had also been gathering domestic messages for three years. Judge Bates found that the agency had violated the Constitution and declared the problems part of a pattern of misrepresentation by agency officials in submissions to the secret court.

A bit later in the interview, Alexander notes that he referred several cases of unapproved spying by NSA analysts to the Department of Justice. But he doesn't know of any time that the NSA has done something illegal. This guy is a master of doublespeak. With interviewers less deferential than comedians, he gets away with it.