If someone were to come up with a good plan for how to control an AI such that people stay in control even as the AI becomes more capable than any person or group of persons, I would not worry much that Altman or Amodei would ignore the plan: both of them know that current plan that they have is severely lacking and that adopting an actually-good plan would reduce the danger that they themselves personally (and their families) incur from the operation of the corporation that they run.
A nice analogy is the serial killer: a large fraction of serial killers are relieved when they are finally caught. They know that what they are doing is wrong, they just can't stop themselves because (for them) killing feels really really good. Analogously, I think Altman and Amodei would be relieved if the government shut down OpenAI and Anthropic because they know that what they are doing puts everyone including themselves and their families at fatal peril, they just can't stop because (for the kind of person who becomes head of an AI lab in the first place) it feels really really good to be the leader of a trillion-dollar-valuation company that is transforming society -- and all the personal power and attention they get from that role.
If he is willing to lie to give his corporation some advantage, he couldn't come up with a lie that would sound less absurd and outlandish to the average decision-maker, who doesn't have much time to learn about this particular technology?
It is more likely in my eyes that he says it because he genuinely worries about AI extinction risk -- like many people do who've studied the technology for a long time.
It is straightforward for industry leaders to avoid living near data centers, but there's no way for them to insulate themselves from the extinction threat -- no way short of somehow eliminating the danger for everybody, which seems quite hard to do. Since industry leaders are as self-centered as everyone else, the extinction threat is what they think about.
Also, you describe the extinction threat as "further out". A lot of us think there is already some small amount of AI extinction risk being incurred every day. I.e., we think the period of danger has already begun.