Another poster linked to this study that states [1]
Existing rates of lead absorption are about 30 times higher than inferred natural rates
It's not the case that all soil is contaminated with lead that then ends up in high levels in food. Top soil is composed mostly of decomposed plants. Plants only take up a small fraction of the lead in the soil. So the contamination of the top of the soil must reach some threshold. Due to leaded gasoline, there is widespread lead contamination in top soil, and I have read many parts of the world still use leaded gasoline in agriculture. Without human activity my understanding is that most soil samples would test very low or non detect and most food would as well. In some types of food (I know this is true of spices and to a lesser extent chocolate), much of the lead in food can come from processing phases after it is already harvested.
We certainly know it is the case that food produced by one producer varies dramatically in lead levels from another due to testing. Some of that may be attributed back to the soil, but it still goes to show that we could be testing soil levels and avoiding growing in lead contaminated soil.
Thank you for those links. For the nut study, they are studying finished products bought in the supermarket, so it is possible that some of the contamination may come from the processing (removing shells, etc) which is pointed out in the study itself.
[1] https://sci-hub.se/https://pubmed.ncbi.nlm.nih.gov/14334042/