I've never heard of this. I've heard that autistic people can often overuse pronouns without making it clear to whom they are referring (such as saying 'he did this and she did that' without first stating who 'he' and 'she' actually are - supposedly a problem of the much-debated theory of mind!).
However, having said that, I do like to refer to myself in the third person for fun. However, I only do that with people I know well, who know me and my eccentricities! I am quite aware that it is not seen as 'normal' to do this, so I normally use 'I'.
I've just thought of a possible reason for the theory that autistics say 'me' rather than 'I'. There is a theory that autistic people do not see themselves as agents - that they are passive and don't see themselves as effecting changes in the world, or having any power. They see themselves as acted upon rather than acting (this is a theory - I'm not sure if I agree, but I can see how it can sometimes happen this way). Therefore, it would make more sense for autistic people to say 'me' more than 'I', because 'me' is the object of a sentence and 'I' is the subject'. So 'me' is being done to, and 'I' is doing (eg. 'The ball hits me' versus 'I hit the ball'.)