That's right. Re-rbar also performs that function. Slab on-grade concrete is not considered "structural concrete" as the sub-grade provides the structure. Poor sub-grade you need structural concrete so it will support itself. Then imposed loads have to considered when designing the reinforcement system. There are a lot of inter relationships for crack control. Yes concrete cracks, key is to get it to crack where you want it too, not where it wants too; therefore, fiber is part of that inter relationship same as reinforcement. I have seen plenty of concrete slabs of all types crack all over due to one or more of those items being not done right or done wrong.
One common example is control joints: If they are cut the morning after placement of the concrete, to bad the cracks where they want to be are already there even if you can't see them. Wait a few days. That is why on large dollar projects they have Professional Quality Control and Assurance at all stages; from the raw ground to the end of the curing process. Small jobs like the OPs, he is the QC. It is not arduous to get good concrete, just takes attention to detail. I can show you many slabs done 30-20 years ago with no re-bar or wire mesh that have no visible creaks today. I did a driveway at one of my houses, 24' wide 60' long full 4"+ thick, 4,000# concrete dosed with fiber and 5% air entrainment. 30 days after placement parked my 40' motor home on it and drove a loaded ten yard gravel truck over it. I put my money into the sub-grade.
Read one or all of those books.
Ron