"Yes, it's possible the technology respects your privacy."
If you can suggest that Amazon Echo is potentially listening and transmitting the data to Amazon even when you don't explicitly say anything, the same can be said of Apple and Siri.
I take your meaning, in the sense that there's no inherent reason to trust one but not the other; but I think that it's fair to say that there's a big difference between:
Hey, wouldn't it be handy for our users if we started storing and pre-processing audio *before* hearing 'Alexa', so that we're ready to respond instantly? Let's quietly take down the text that says that we don't do that.
(which is a plausible reasoning process somewhere down the line) on the one (Echo) hand, and
Hey, wouldn't it be a good idea if we ignored our users' explicit election to turn off a feature?
Unless you expect random or targeted surveillance, if it generally listened and sent packets all the time back to Apple, even if you didn't tell it to, that someone would have discovered this by now.
There's an "always listening" feature, but this is off by default and only works when you are plugged into external power.