We had a very nice didactic at our VA about LGBT qualifications, and how sexuality and gender inform clinical evaluations and care. Asexuality was a category among others for those who lack in sexual desire (meaning it was not guiding factor in interpersonal relationships...these folks functioned well with the lack of sex), but this is separate for those who identify with both male and female traits or desires (i.e., someone who is transgendered or even someone who is bisexual...both being different qualifications of sexuality also). I also agree with MBellows that arousal does not constitute self-identified sexuality. There used to be a LGBT-Q where "Q" stood for Queer (not the in derogatory sense, but in the fluctuation of feelings from one day to another, so this Q became "Questioning" in some of the sexual orientation literature). Asexuality is even different from Questioning as it takes volition and biological need in play, and from what I've learned, those who identify as Asexual just don't view sexuality or procreation as a priority in their repertoire, and may be entirely satisfied with non-sexual relationships.
Futureapppsy2, you're probably not finding anything in the literature because all of this is fairly new in the field. You can try to do a pubmed search, but the person who chaired our didactic is a psychiatrist and he said that historically the issues of androgyny, asexuality, transgenderism (again, all mutually exclusive and not meant to lumped together) initiated in the medical literature because physicians were tasked with responsibility of caring for these folks via medical procedures and treatments (probably starting around 1970s is when it became more widespread regarding the start of ethical responsibilities to the patient and treating clinician).
Provocative but appropriate to the topic, there could be those who identify as asexual but still self-stimulate...then the question is who or what do they think about when/if they fantasize during self-stimulation. That may be a clue as to their existing sexual preference from a psychological point-of-view, whilst the individual claims to be asexual. However, there are some who do not self-stimulate and go about their days with the lack of sexuality in their being. To me (based on what I learned) that is a someone who is truly asexual in the sense I think you are inquiring about.