Asexual-identified people, just like trans people, are trying very hard to pretend to all be some ideal type. I've seen:

• People trying to be special, especially the "asexuality is a spectrum" crowd
• People who don't seem to actually have any sexual interests
• People who have not yet had the "Great Homosexual Awakening"
• People with exclusive paraphilias--they have no interest in sex (how they asexual crowd defines asexuality,) but they do have a sexuality
• People who need the services of an endocrinologist or other medical professional
• Confused people
• Personality disorders resulting in poor interpersonal functioning and lack of desire thereof

Of course, none--save maybe the first bullet point--of the above would prevent somebody identifying as heterosexual, either.