Forget that rule - it makes no sense. Both forms can be used with any type of verb. The present perfect tells us that the action or state connects both past and present so eg: I've liked horses since I was a child.
(stative verb expressing an action that has lasted from the past to the present) I've answered twenty emails since I arrived
(dynamic verb expressing some past actions which started in the past and have continued up to the present).
Continuous aspect tells us that the speaker/writer views the action as continuous but temporary. So the present perfect continuous tells us that the speaker is talking about something with past to present reference, but which s/he doesn't necessarily think is a permanent event. So eg: I've been feeling ill for the last three days.
(state) I've been answering emails since 9 o'clock this morning.
Obviously the speaker considers that sooner or later the illness will pass / there will be no more emails to answer and so chooses to present the situation as temporary.
Notice that I say "chooses to". The use of different verb forms always depends on the perception of the speaker. My favourite example of this is the following. I left England in the early 1980s and moved to Italy. After a while it was clear to me that the move was permanent and if I was talking about it, I would always say eg : I've lived in Italy for the last ten years
. However, for my mother, it was very difficult to accept that I wouldn't be returning to live in the UK, and for years afterwards she would say Susan has been living in Italy for the last ten years
. The event we were describing was the same, but psychologically I saw it as permanent while my mother went on hoping it was temporary. Hence the different choice of verb form.
For a more detailed explanation of aspect, have a look here
, and for a critique of whether there really are such things as "stative" and "dynamic" verbs, see here