This is true: though Obsessive Compulsive Disorder is a common co-morbid diagnosis with ASD, even those without this anxiety disorder may show some obsessive behavior given the right circumstances.
The obsession part of OCD is common experience for autistic people, especially obsessive thought related to past slights, insults, teasing, bullying, exclusion and unrequited love.
The person can find themselves reliving the embarrassments, pain and humiliation over and over again. The thoughts become intrusive and the individual can't seem to shut them off.
What to do?
This kind of looping, perseverative thinking can cause great anxiety.
It's important to get help from a professional who knows how to help someone with verbal autism/ Asperger's/ ASD Level 1.
This means you'd need to find that rare expert who understands what it means to have a communication disorder in spite of being verbal--and they'd understand the slow and specific approach that is essential to build trust.
Perhaps you are autistic and this resonates with you. If that's the case, or if your loved one on the spectrum is looping over an incident and just can't break free of the anxiety it is causing, support from such a professional may help to break the cycle.
If you are going to invest the money, time and emotional energy to address the trauma caused by these kinds of repeated social injuries, try to find someone who knows what they're doing.
Therein lies the real challenge