I've seen deep sand beds described as something as deep as 4 inches. It kind of depends on how fine ( or, rather, how dense) your sand bed is. It's all about that aerobic/anaerobic relationship. Same as your experience with freshwater, in that way. In a planted tank, you get that anaerobic business happening pretty quick because not much is stirring it, you've got mud and other sludge like decaying plant matter that is very dense, and then you have roots pulling nutrients from it as well.
I consider my 3-4 inch deep sand bed a DSB insomuch that it is visually deep. That's why I said there are those that may argue mine is not a true DSB. I do not expect to see a lot of anaerobic activity in my sandbed at these depths. The only reason mine is the depth it is - is because that's what two bags of sand filled it up to. I put no more thought into it than that.
Unless you are planning to go past 3 inches, I'd say you can stop sweating this one