Yes, that is correct with two caveats. You need two individual working PATS keys to program a third. Places like Home Depot, Ace, Lowes, etc can cut you a working PATS key but it’s a clone key, they program it to clone your original, so even though both will start the truck, you can’t use the clone to program a third key because the computer sees it as the original key and not a separate. Hopefully the locksmith is smart enough to program it as an individual key and not a clone. Forscan and an adapter cable can be used to program keys on your own for most Fords if you get the extra license. You can, however, have as many clone keys as you want, but you have to be careful if you buy blanks, not all blanks accept full individual programming, some are clone only.
Caveat #2 is there is a limit to individual keys that the system holds. I want to say it’s 8 keys and like 12 fobs. If you had 8 individual keys programmed to the truck in its life, you can’t add another individual without deleting keys from the computer. My green Ranger I got with one working key, but when I got into the computer, it showed 5 keys. I don’t know if things have changed, but at the time you needed two good individual keys to wipe the old and start over, so I did. There was no way with Forscan at the time to wipe individual keys, so it was delete them all. You must have two good individual keys for a full wipe though. Anyone who has the other 4 keys that were lost with prior owners no longer work that truck