It's actually not a triphthong, because the r is not a vowel. Rather, it's a syllabic consonant: http://en.wikipedia.org/wiki/Syllabic_consonant
The IPA represenation is not [ə], but rather [ɹ̩]. (There's a tick under that ɹ).
And, to be fair, your statements are accurate for British dialects of English that don't have syllable final rhotics, but the original article was about American English.