I am confused by this rule:
606.1. Some activated abilities are loyalty abilities, which are subject to special rules.
Is this correct?
Yes, it's correct. The rule you quoted implies that loyalty abilities are activated abilities. And since there is no rule that makes an exception for loyalty abilities, they can be countered like any other activated ability.
Remember that countering an activated ability only stops it from resolving. The costs paid are not returned. So the loyalty counters added or removed are not restored.