audio encoding technology has come a long way, even just in encoding mp3s that would still play on a Rio. Back in the early days, bitrate mattered greatly but so did encoding software used. Encoding software ( and settings) still matter, but most have improved to the point where bitrate is less important. A modern 128kbps encode is generally hard to tell from 320kbps, and might even sound better than some earlier 320kbps encodes. Plus, modern VBR, even maintaining an average bitrate, can make a huge difference. Once upon a time it was either VBR with no bitrate control or a fixed CBR. Nowadays, you can use VBR with some buffering to put the bits where they're needed most.
Having said that, the source material matters too. Looking at the NPR selection, they're almost all trivial to encode assuming a reasonable bitrate (64kbps might be obvious, especially if it's mp3 and not AAC, but 96 or 128 might be hard to tell from 256 and above). Even the few more difficult to encode pieces aren't really that heavy on the sorts of combinations that lead to noticeable aliasing when using perceptual audio encoding methods. The NPR setup is using 128kbps, 320kbps, and uncompressed WAV - with any modern software these should be basically indistinguishable for nearly all sources. Mobile streaming services are far more likely to use 64kbps and/or 96bkps as their lower tier, though it helps that some of them use AAC instead of MP3. If the NPR test wanted to really test your ability to discern bitrates, they should have had a lower bitrate in the mix.
Comparing for example, some more difficult to encode (due to the artificial nature of sounds used) source, like some (but by no means all) Daft Punk songs as an example, using Amazon Prime music, the lowest setting is audibly garbage, the middle and high settings are closer but in some sections I can tell the difference.
However, listening environment (which includes the listener themselves) and playback device make a bigger difference once you get past the lowest tier of audio encoding. I used to listen to streaming audio using the analog aux input on my Mazda 3, but once I finally got a decent bluetooth adapter (which also is connected via aux in, but is using BT from the phone instead of the phone's headphone output), the difference was quite noticeable, especially in the low end. The phone's headphone output just wasn't designed to drive a car's aux in, but instead a much smaller load like ear buds.