Does updating iPhone successfully proves it is Factory Unlocked?

I was being told that my brand new iPhone 5 is Factory Unlocked n from an authorized source! However, some IMEI checking websites claim it's SIM is locked or it's under a Contract which expires after 2 years. To verify this, I successfully updated my iPhone 5 to the latest iOS version today (without connecting to iTunes thru Laptop or anything) directly using my wifi!

Does this PROVES that this iPhone 5 is factory unlocked & from an authorized apple source?

Can I use it now anywhere in the world on any network carrier without any locking issues?

What happens when the contract which is mentioned on www.iphoneox.com when checking my IMEI number expires later? Will my iPhone get locked after 2 yrs when this contract expires? Can I not use it anymore on any other country's network carrier?

PS: I didn't buy my iPhone 5 with any contract with any network provider! So I don't actually wanna believe what this Sim Lock Checking using IMEI websites are saying about the "contract" or the "sim locked" thing!