There does seem to be this notion that being "too hygienic" is a negative thing because it doesn't train your immune system.

That's only kind of true. Exposing a healthy person to small amounts of weakened virus tends to build immunity. Exposing the healthy person to large amounts of the virus overwhelms the immune system and may not even lead to a strong viral immunity.

If I had to guess, eating rotten meat is something that indigenous peoples have adapted to over time (and some individuals died along the way to that adaptation) and they are resistant to the specific things in rotten meat that make modern day humans sick. I think it would be wrong to suggest the rotten meat eaters are somehow better off for doing this, or that they have stronger immune systems in general.

Immune systems aren't like a muscle that you can repeatedly train to get stronger and stronger and stronger ad infinitum.

Immunity also comes at a cost. This isn't talked about often. But it's not "Free" for your body to learn and maintain immunity to specific infections.

Just look up the Hadza tribe's gut microbiome.

https://pubmed.ncbi.nlm.nih.gov/36238714/ https://www.nature.com/articles/ncomms4654

That's probably as close as you are going to get to truly paleo diets... not paleo-bros that eat only bacon, butter and meats.

I see how easy it would be for me at least to assume they had better immune systems from eating the spoiled meat. If true our modern immune systems are most likely way less effective than theirs at that time.