Actually this information is completely correct and has been confirmed.

Different people have different chemical resistance to certain Chemicals and neem isn't harmless.

Totally correct information. And it's systemic which means that it actually is stored in the cells of the plant making the entire plant toxic.

Personally homemade nicotine spray as well as diatomaceous earth and some sand would be about the most you would ever need.

If we can get some more pictures of those bugs we can figure out what kind of issue you're having and then settle it.

Personally I think it is some fruit flies and you just need to put a layer of sand about a half an inch deep I believe on top of the soil of your plants. Also add diatomaceous earth that is food grade will help add extra micronutrients that are chelated for easy use by your plants.

The diatomaceous earth actually works like broken glass against the carapiece of all insects. Getting through it wounding them and removing them from the equation.

Beautiful work to keep it up!