In reality, there are not two, but four elements to empathy.
1. Reception of information: Reading another person's state of mind.
2. Compassion: Wanting beneficial things for another person.
3. Emotional mirroring: Instinctive copying of emotions expressed by another person.
4. Emotional Expression: Communicating one's compassion to another person.
The cognitive/affective model is very much deficient because it does not take communication into account and does not differentiate desire to help from emotional mirroring.
These are the incorrect assumptions that need to be corrected:
1. Reception of emotional information does not have to do with compassion, but with communication; it is, in fact, only peripherally related to empathy. Not being able to understand another person's emotions is unrelated to whether or not you care what they are feeling; mixing this into "empathy" confuses the issue. It is like accusing someone of not caring about their friend's recent bereavement because they were not informed of the loss and thus could not express their condolences.
2. Compassion does not need to be emotional. There is often--probably, usually--an emotional element; however, desire to help can be quite cerebral and dispassionate. In fact, some of the most compassionate people--doctors, paramedics, firemen, etc.--are specifically taught to keep their emotions out of the picture so that they can help more effectively. It is incorrect to assume an empathy deficit in an autistic person whose compassion is rational rather than emotional. If the person desires to help another person who he knows is in trouble, then whether or not he is emotionally moved, he is being altruistic--that is, compassionate.
3. Emotional mirroring has been shown to be less likely among autistics watching NT emotional expression. This phenomenon probably helps NT children learn compassion because if an NT child witnesses someone else being hurt, they will feel an echo of the pain themselves. Emotional mirroring forces them to learn compassion. That autistic children mimic emotions to a lesser degree is not necessarily indicative of a lesser degree of compassion, however, because without that constant flood of emotions from other people, autistic people do not become used to functioning in the presence of others' distress. This effectively means that it is difficult for an autistic person to understand that someone else is feeling distress, but because they are not used to it, others' distress tends to affect them to a greater degree once they understand. There is also much less need to actually witness suffering for an autistic person to feel compassion; merely hearing about it is enough.
4. Expression of compassion is often the NT measure of empathy because in the NT world it is assumed that one will be able to read and understand another's emotions instinctively. Under this assumption, empathy can be measured by simply looking at whether or not the person who witnesses another's distress responds to it in a pro-social way. This idea that "if you don't respond, you don't care," has been taken for granted to the point that it is being used as a measure of empathy in experiments--but these experiments can only be valid if it can be established that the information about the other person's state of mind and experiences has reached the observer. In most cases, that is not tested. Autism is a disorder that affects communication--including communication of sympathy and desire for another person's well-being. Assuming that an autistic person is not compassionate because he does not express sympathy is like assuming that a paraplegic is not polite because he does not stand to greet a visitor.