Dare I guess that you have not worked at a line station or two?
When the head of training at DFW said, "There is no way that any un-licensed mechanics are working the line, and especially signing log books off. " did he mean actually working the terminal or working shops and checks at a line station?
I will not name names here, but it happened for years. Don't know for sure if it still is, now, since it is not on my radar. I do know they quit hiring unlicensed mechs at my line station some time ago, but continued to hire avionics techs with FCC licenses for a while longer. Some of the unlicensed mechs and avtechs have retired, though. One Repairman I can remember even went on field trips by himself. Very often, in fact. So yes, he signed off log books. Without anyone inspecting his work.
I think different people had different situations with management. But, it was not uncommon at all for unlicensed mechanics to sign off work cards at a line station.
When license pay became larger, most got licenses, but not all. Never understood why they would not want the license pay. At one time, a 2nd class FCC license was good for single license pay, and a 1st class was good for double license pay. Don't remember what happened to those 1st class FCC license holders when their license was changed to a General license, just like the holders of 2nd class FCC licenses. Most avionics techs just went ahead and got A&Ps, anyway so they could work the terminal and go on lucrative field trips, so it became a non-issue.
Didn't some unlicensed mechs in overhaul get "Skill Pay", at the same rate as license pay, at one time?