Years ago a friends wood shop went up from oily rags hang drying on hooks and they were fairly "dry".

27 years ago my woodworking shop was in a large warehouse with different businesses, including 2 other woodshops. One of them oiled with Watco oil. The oil dripped through a small hole in the table and onto a stack of paper wipers. Warehouse burned to the ground.

When I was in that building, before the fire, my rags were put into a drum with water until they could be disposed of.

These days the finish I use on my products is a combination of Boiled Linseed and Alkyd Varnish. The paper wipers go outside away from the shop into a wire circle 2' in diameter and 4' high. They get rained and snowed on. There are occasions in the summer when some of theses will spontaneously combust. Sometimes it will be in the layers a couple of years old.

You're right about the oxygen but linseed oil doesn't really "dry". Boiled Linseed "drys" because of the process and added drying agents.

Personally, I only use paper wipers and they go outside immediately. Having gone through a fire probably makes me overly cautious but the results can be devastating.