This highly misleading. Yes, DTA has that "Access your data for all websites" permission. It is required to make the "DownThemAll! All Tabs" feature work. Without it, DTA would only able to work on the presently active tab.

I'd rather have a more fine-grained permission, but that isn't offered by the browsers.

Anyway, the privacy policy clearly states that DTA does not collect any data, it does in fact not collect any data, and the add-on is open source so you can check that for yourself, the code inside the shipped package is not minified so you can check it as well.

Furthermore each version is reviewed by mozilla, and actually reviewed thoroughly as a requirement for getting the recommended badge. "Stealing" user data would be against mozilla policy and they wouldn't approve such an add-on. Not that I ever would do such a thing, and I've been doing DTA since 2006 so I have a little bit of a track record of NOT stealing user data.

So, use the add-on or don't. But please do not insinuate falsehoods.