I would say that rather than saying that ASD people either can not tell lies, or are compulsive liars etc.
I would say a better explanation would be that people with ASD follow rigid thinking patterns, which perhaps has been installed in them during their upbringing (perhaps by the parents).
So, if a person with ASD's parents are the honest as the day is long types, and are a great influence on the ASD individual, then the ASD individual is likely to grow up being extremely honest, and rigid in his/her behaviour doing so.
On the other hand, if a person with ASD is brought up from day one by parents who are manipulative sociopath liars, who teach the child who is rigid in terms of thinking that the solution to every situation is to lie, then this behaviour trait is picked up or conditioned into the ASD individual, who may end up following this behaviour rigidly.
To use the common computer metaphor, the ASD individual is like a computer that during their childhood has an operating system installed on them. The operating system determines on how the ASD individual interacts with the universe and is rigid in its nature.
I personally am honest to a fault, which i note, gets me into trouble many times over life.
As Frord mentioned. Unfortunately for us ASD types, due to co-morbid mental health problems that causes us to be perceived nervous, and due to our inability to keep eye contact (or in some, causes us to stare intensely at people in the eye, which i note can also be very unsettling), we are often perceived as automatically guilty based on looks and mannerisms alone.
Our body language to the police for example may say we are nervous, and suspicious. Something about how we present ourselves that is not quiet right, which often equates to GUILTY regardless as to what facts are coming out of our mouths.
In modern terms however, i believe in countries such as the US, these newly discovered facts about ASD may give some grounds to an appeal if prosecuted for any crimes before this date.
In the UK, however, appeals are extremely unlikely, as they are costly and need to be paid for by the defendants pocket. In many cases of people with ASD, we find ourselves in extremely poor financial circumstances, so are very unlikely to ever be given the liberty to seek justice for the wrongful punishments imposed on us by incompetent, uneducated and in some cases, corrupt law enforcement agents and agencies.