If the quote was real, Iwata acknowledging that Apple were a possible "enemy of the future" basically means that he sees the possibility for Apple to disrupt Nintendo's handheld business in the future if Apple continue to increase their focus on games. As has been said earlier in the thread, the iPod Touch could very well become "good enough" in terms of the games it offers and then become a direct competitor to the 3DS in the future.
Now I say iPod touch and not iPhone because it's the iPod Touch that really allows Apps to flourish. It's a system built with Apps as one of it's main draws and the advertising for it is all about Apps and more specifically, the games available on the App Store;
iPod Touch: "The funnest iPod ever"
The fact that Apple are playing up the "fun" aspect of the iPod Touch is obviously seen as a threat to Iwata as he has continuously mentioned that Nintendo is in the business of creating "amusement products." One can see how the iPod Touch and the DS and soon to be 3DS are not mutually exclusive, their IS overlap, just as their was with the DS and PSP.
I think the main difference between Apple and Nintendo is that Nintendo had the experience and knowledge to pull off the disruptive strategy in the gaming industry rapidly, whereas Apple are still feeling the waters, they are going about it very slowly and some have commented they are finding themselves in the gaming market "by accident."
Whether the quote was genuinely Iwata's or not, I think he knows that Apple is a possible threat for the future growth of Nintendo. The 3DS and it's features will be telling of what kind of plan Nintendo has of fighting (or not fighting at all) Apple and also disinterest in Nintendo's current offerings.