If the default is just that, a default value, that is not "business logic." If you insert a record and set an integer to zero, is that logic? Most modern languages (e.g. pretty much anything C-based) would default that to zero anyway. Does it really matter if you default it to one instead?
The way I see it, "insertion logic" goes in an "after insert" trigger. Code executes, it calculates a value, and sets it on the new record. For example: on insert, field C is set to the sum of fields A and B, instead of some fixed value such as zero. That is "insertion logic."
"Every new record gets a value of 'baz' in the 'foo' field if not already specified" is not really logic in anything but the most trivial sense of the word, certainly not in a complex program.
What uses of the default clause when defining a column are not considered having business logic in the database?
Since you specifically mention "default clause" which would mean "not a trigger," I say all uses of the default clause do not add logic to the database.
As an aside, most databases treat default values as default constraints. In other words, "
null is outside of the acceptable values for this field so set it to something within the set of acceptable values instead." If you look at it that way, a default value is almost the same as specifying a range of values for a field. Set it outside that range (
null), and you get a default value instead.