Meh, I feel like you're taking a common expression and reading it too literally.
"I couldn't have made it to the top of the mountain without these specific hiking boots" doesn't mean it was literally impossible without that exact brand of hiking boots. It means they like the boots, it made the experience better for them, and they think the hiking boots are better than comparable ones.
I don't think the CTO is claiming that Stripe is solving a problem that would be impossible to solve without AWS. He's saying we wouldn't be as well positioned today if we had to solve the problems that AWS solves ourselves, or by relying on their not-quite-as-good competitors.