I think you're both right
Hophead and Industry Hack, you are both making sense to me. I think you're saying that under good circumstances, you should be able to simply turn the adjusting screw. But if there is too much pressure from the spring, or the screw has Locktite on it, you might not be able to turn the screw and to attempt it will result in breaking . . . something. In that case the thing to do is to relieve that pressure.
The one thing I don't understand is, would releasing the noodle have about the same effect as releasing the spring? All went well when I released the spring. It was just a little tedious to do that about 5 or 6 times before getting the brakes centered just right.
In fact my Tekro brake was treated with blue Locktite, and the screw was the phillips/slot head. It wasn't that hard to mangle the screw.
The mechanic in question seemed like a somewhat hysterical individual, prone to sweeping statements and overassertiveness. Direct quote: "Well, I guess I know more than all those websites and Tektro, don't I?" I think if it were generally necessary to release the spring, that would be clearly stated somewhere by someone.
Tektro is low end, huh? Sigh . . . Nice folks though.