Well, there's some truth to your statement but there are many factors in between those two points. First it depends on how severe the damage is to your anterior cruciate ligament (ACL). A minor tear can be treated with rehab. This is especially true if you're not an athlete or exercising at intense levels.
Studies do show a tendency toward cartilage damage in unstable knees. This means the ACL is deficient and not doing its job. The joint slides around more than it should, putting stress on the meniscus and other joint cartilage. Under the increased load, wear and tear on the meniscus could end up in a tear.
Only one study has been done that shows the need for a total replacement (TKR) after ACL injury without repair. A small group of olympic athletes in the former East Germany were treated without surgery and returned to training. Doctors followed them 35 years later and found out that all of them had a torn meniscus. Half had a total knee replacement.
Long-term studies of everyday average people with an unrepaired ACL have not showed these kinds of results. They do report an increased pattern of osteoarthritis in the unstable (unrepaired) knees. The risk of a TKR is present but not a certainty.