The thing is, almost every time when people put negative conditions (that you must not meet in order to qualify for something else) every condition is disqualifying, and that idea is expressed with "or". Which of these sounds more natural to you?

"You can have some of my pie if you don't have eggs, sausages, and bacon."

"You can have some of my pie if you don't have eggs, sausages, or bacon."

To me the second one sounds more natural. The first one sounds very unusual. I can have pie only on the condition that I don't have all three things? Okay... It sounds so strange because no one ever says that. I can't see someone using "and" there if they didn't mean it, because it's such an unusual grammatical construction.