Is it true? No. And that statement that you were given ("you CAN'T be an Aspie") was a load of crap told by someone without any insight.
Example: My diagnosed aspie friend has a WAY larger sociallife than i have, her social skills are seen as normal.
Having Aspergers/HFA is not as clear as having a broken bone or having cancer where there is clear undisputable evidence of it. The reverse is also true; Either you have a mild autism - or the opposite. There is no high functioning broken bones or low functioning deadly diseases.
Thats why the wikipedia article on AS/HFA says "Some individuals" or "Many individuals..." or "a few individuals..." and not "Everyone".
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"It is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring" (Carl Sagan)