Is there a certain pronunciation pattern that when the same vowels meet together—in this case schwa plus schwa—the two combine together and so there's no room for intrusive /r/? Or did I just hear wrong?
(1) It's hard even for native speakers to 'hear correctly'; you can get most people not trained in language study to claim to pronounce letters they simply haven't pronounced. Hence most English speakers will claim (wrongly) to pronounce 'p' the same way in pit and in spit.
(2) You're getting into tricky territory, because phonetic 'segments' (http://en.wikipedia.org/wiki/Segment_(linguistics)) are not nearly as clean-cut as we imagine them to be.
(3) There are lots of things that can happen when two similar sounds collide: You can get r-insertion. You can get dropping of the second sound, without or without lengthening of the first sound. Or you can get -- and this is an interesting one for the consecutive vowels case -- the insertion of a 'glottal stop'. In English this sound is generally unknown since it is never written down, unlike some other languages.
For example, I am pretty confident that all native English speakers, including myself, will automatically and unconsciously insert a glottal stop when spelling the word BEE out loud. The glottal stop goes where the hyphens are:
Otherwise it would not be possible to distinguish the letters. Unfortunately I couldn't get your audio to work, so I can't comment on that, but you can read more on the glottal stop here: http://en.wikipedia.org/wiki/Glottal_stop and