You can use a verizon iphone 5 on at&t because it's "allowed" to access at&t's type of network, but only the slow 3G network, not the fast 4G network.
The at&t iphone 5 on the other hand, cannot access verizon's network because verizon doesn't allow it.
Just pretend you're buying a car from america versus Afghanistan, where the American car is verizon and Afghanistan car is at&t. The american (verizon) car works in both countries because it meets both the strict american (verizon) clean air regulations as well as no regulations in Afghanistan (at&t). But the Afghanistan (at&t) car wouldn't be allowed to run in america (verizon) because it puts out too much pollution.