|Darksol the Painbringer|
The general rule cited above states that when you are restricted to taking only a single standard or a single move action, you can still take swift or free actions as normal.
Being nauseated restricts you to only a single move action.
Specific overrules general is a principle to apply when two rules disagree, but I don't actually see where the second rule is supposed to be in disagreement with the first, much less specifically overrule it. The second rule merely provides one of the circumstances to which the first rule applies.
Unless we're talking about the certain types of free and swift actions that nauseated does specifically address - e.g. spellcasting - in which case yes, the specific nausea rules about those types of free or swift actions would overrule the general allowance of free and swift actions.
In the general case of being limited to a Standard or Move Action, you can take Swift, Free, and Immediate Actions as normal, and you're correct.
But, "only" is a much more limiting factor when it comes to the Nauseated condition. When it says "The only action such a character can take is a single move action per turn," the specifics of the Nauseated condition, which say you get the move action, and nothing else because it otherwise breaks this rule, supersedes the general rules given for restricted activity, which say you can take Swift, Free, and Immediate Actions as normal.
That's basically a step-up from, other than the can take a single move action, the Helpless condition.