It is definitely not indistinguishable, both because "someone with this rating shouldn't be winning like this" and because engine moves look very different than human moves, especially at lower ratings.

Interesting.

How true is that at the top levels of play?

What do you think the success rate is for online players telling an engine from a human? 1% 99%

At top levels it gets closer -- often human play is compared to engine play and people will discuss which moves were 'engine-like' vs 'human', and a significant achievement would be to play the engine moves on every turn. Although it should be said that engine moves are not always necessarily the best moves positionally, nor the moves with the highest win % versus a human (because you can 'trick' a human, whereas the engine can't trick itself so it will never prefer a move like that)... but they are always the best moves tactically.

In middling ratings, if I was allowed to look at the engine (in a Lichess replay for instance) I'd guess I can tell a player using the engine with 99+% accuracy. People _always_ lose on tactics (or misplayed opening lines, misplayed endgames, etc). Engines never do. At high ratings I assume this goes down, especially if the players are playing 'boring' draw-ish lines, in which the best moves are fairly obvious most of the time.

Thanks for breaking down how this would actually work in practice. As an amateur player, I don't think I personally would be able to tell the difference between playing a much better player and a good bot, or a bad player and a bad bot.

A cheating player isn’t going to have equivalent elo when cheating and not cheating.

I’m pretty sure that just proves that your mental model is too simplistic to explain the real world.

This is true for everyone and everything.