[asQuirreL]

I've got to be honest, I answered yes to both your rhetorical "are these algorithms?" questions, which I'm guessing was not your intention. It would help if you gave some examples of what is missing in each case (in your eyes) disqualifying them.

With the SQL example:

I don't think a set of rules is disqualified from being called an algorithm if it's implemented using some other tool or process, because we do this all the time: when programming, we split up implementations into functions, or we could have used the standard library's sort function too -- I would still consider it an algorithm no matter how the "sort the results" step ended up being implemented.

If the result is wrong, it is not necessarily because the implementation of SQL's ORDER BY is incorrect (it could be but it's unlikely for a popular SQL implementation), and if you know that the the rules are incorrect then I agree, I definitely wouldn't blame the sorting algorithm (at least initially, although it's possible it's also be wrong).