I did a fresh install of Ubuntu desktop the other day and there are Amazon icons on the sidebar by default. I didn't opt in unless it was maliciously bundled with another option.
There is a conflation of issues here. There's two separate Amazon things: (1) The launcher on the dock by default -- annoying but not subversive -- and (2) search integration, where your local searches would also query Amazon, which used to be enabled by default -- a privacy issue which caused some controversy a few years back. Great grandparent was talking about (2), specifically, so in that context I understood the grandparent to mean only it. However, the wording was certainly unclear if you weren't familiar with the controversy.
And not just downvoted but flagged... Anyways yeah, I tried Ubuntu out and the Amazon icon is there and isn't easily removed. Plus Unbuntu has auto-on telemetry or crash reporting as far as I understand.