The 5% or less of water myth has been around for a while but I am extremely skeptical. Here are just a few of the real world examples of products I have seen contamination with low water/anhydrous formulations.
Eye shadow - anhydrous microbiological contamination (we guessed that it was a thumb print contaminating the powder) as a result of a production issue when packed. This was a preserved product but the preservative system was overwhelmed - which lead to another investigation into the manufacturing facility, but that’s another story.
Humidity causing microbiological contamination in a body powder type product.
I sent a cream based product for microbiological testing that had ~3% water in it because I was skeptical it would be safe on the market - it was already contaminated and failed challenge.
These are just a few of the examples I have seen over the years that I can remember off the top of my head.
Now I’m not saying that you can’t create some lovely formulations using low aw as a way to preserve products but this needs to be tested not extrapolated as RSullivan and Perry states.