I think being an idol is about media presence sure - but not just the fact that they are there - how they say things and act in/on TV and press releases etc etc. contributes to their idol-ness.
In this case, I think Perfume has most all idols (that I can think of for sure) beat.
I sure don't consider them Idols, because they dont act like them. The key part is that they are hardly "acting" in the first place. I mean, from what ive seen of japanese TV and interviews, but really all tv & interviews that are live and or scripted, acting is part of the job.
Perfume doesnt get a b**** slap from Nakata or Universal everytime they are seen with a guy and threatened to be kicked from the group, because the group was actually made by them. They didnt go out individually by some label and be specifically picked apart to be in an idol group. They didnt even sign up to be part of "Perfume". Perfume is an electropop unit, not an idol group. You can argue it all you want I really don't care, but thats how I see them. When I first heard Perfume, I hated their music, but now they are one of my favorite japanese groups of all time, hell one of my favorite music groups of all time! They arent young teenagers-adults who were born and bred for the role, dreaming of how some day they would be "idols" they grew up with hardships in real life and the music industry and faced disbandment, ridicule, and lack of faith from all sides.
+ As i kinda said before, they aren't a female idol group that is subservient entirely to their fans and management. Heck, they invite other groups for lives and take risks. They do have a squeaky clean image, but it feels more like that's their own choice, their Perfume no Okite. It seems like a sacred bond of trust between the three of them to keep the integrity of the group together. I mean, their management is lacking in image development but they don't appear to be typical slave drivers of the pop music industry - at least in regards to perfume. (But yeah, especially their hair-costume designs, but they are just super cautious and personally I wanna see some outfit/hair changes like the one Kashi has in that R.E. cover. I mean... dat forehead!)
By the way. Party Maker is 7:20 long, Furikaeru to Iru yo is 6 minutes, Enter the Sphere is 3 so it may or may not even be a typical perfume intro.