It's entirely possible to prevent cracking in a typical residential garage slab - it's just takes a little more effort. Understandably, most people just cut control joints so they don't have to deal with it.
The trick is to mitigate shrinkage, which is the primary cause of random cracks. To control shrinkage, you must control the water, more specifically the mix water. You want to minimize the amount of water used to batch the concrete and then minimize the loss of mix water after placement through proper curing.
The conventional wisdom that 'there are two kinds of concrete...." is complete ****. If you're willing to put in the effort, there is no reason you can't construct a crack free slab.
Those that suggest that steel reinforcing is a benefit are correct, but rebar or mesh do not prevent cracks. They do serve to hold everything together and preserve the structural integrity of the slab if cracks do occur.
With respect to the contractors comments about water freezing underneath being the cause of the cracking...........well, that's just more ****