Um, no.
You are wrong
Look into Adaptive Bitrate Streaming [0].
From what I’ve read HLS does work this way, when combined with Adaptive Bitrate streaming, the segment files are swapped midway depending on user device and connection quality (with each video segment being kept encoded at various qualities to change between as connection quality varies)
The screenshot thing is a fair question tho, why pausing leads to higher res. I think some players, do it custom, for User Experience, so that they can produce clean screenshots on pausing. I’ve seen YouTube do it for sure.
But for you’re main point, you’re objectively wrong, adaptive bit rates and swappable segment files are a thing.
Edit: (Don’t worry about it, being wrong is good hehe, i was wrong 7 times today while doing my work, helped me learn new things 3 out of those times, you helped me question myself and look back at my knowledge too, it’s been dusty for a while. Have a great day!)
[0] https://en.m.wikipedia.org/wiki/Adaptive_bitrate_streaming