Amazon always tried to give the impression that they use AWS but (at least in early years) those were half-truths (i.e. statements vague enough that if you squint at it one way you can read "Amazon's internal systems are build in AWS services" and if you squint at it differently, they might just as well say "AWS's servers are hosted in the same data center as Amazon's servers"; public perception was the former and the reality was closer to the latter).
That, of course, doesn't mean that 37 Signals' advice isn't good, just that this is not an example that confirms that advice.