I don't know, at least not yet. I've only been doing this for two years, maybe they didn't have time to gunk up.
I use the oil I buy to lubricate sewing machines. Not only I oil everything that is metal against metal, I rub some of it on every spot it I consider it needs protection from rust.
I stopped worrying about too much oil when I read on a typewriter repair course from I don't know what decade that after drying in an oven to put it in an oil bath to lubricate and protect metal surfaces. I won't go to those extremes but made me realise that if I put too much oil worst thing it could happen is that the typewriter will need a new cleaning next year.
I imagine that if they managed to convince him is because he wasn't feeling too well.
In other words, maybe what killed him wasn't having bath but what made him change his mind about the bath.