That is correct but I don't believe it needs tweaking. It appears they are going under the idea that if the person could pass the thicker test, then he still posses the skills to pass a thinner test.
Granted if it's only been less than a year since the lapse that may be true, but if it were 20 years then he most likely may have lost those skills.
In the past if the person didn't get re-employed by us within a year or two, then I would re-test him with the 1" thick test even if he had the cert previously, just for that reason, to assure he still had the skills needed to weld properly.
Also keep in mind the code is the minimum required-is a company wants to require more than the code, they have that option.