It is not making the key! It is matching the chip in the key to the car.
The procedure in the Owner Manual is for ADDING a key. If you don't have a working key it MUST be done using a computer like a Tech2.
Any procedure you see on the internet that is not the same as the one in the manual is just BS. I have personal experience.
If the locksmith could not do it they either have the wrong equipment or don't know how. If there are already 10 keys matched up to the car they need to be erased from memory so you can start over, most techs don't know how.