A more accurate summary is:
The people asserting that one should wear techeiles have done a marvelous job bringing a plethora of rayas ranging all over shas that form a legitimate basis to wear techeiles. The people (person?) claiming that there is still a basis to not wear it do so on the basis either that: 1- you’re following the psak of one of a few gedolim or 2- you’re following your mesora (which is the same thing, the real difference is the underlying svaras given.) No attempt was made to provide the logic by which a mesora says not to, because it is unnecessary to support the argument that the shitta exists.