Bjarne is making the assumption that the engineers used a phenomenological model that had not truly been derived from relativity. The engineers in this view used an ad hoc expression with phenomenological parameters. They then used least squares criteria to determine the best fit phenomenological parameters.
The engineers in his view calibrated their measurements with a large confirmation bias. The 'relativistic formula' was induced from observations, not deduced from relativity. They calibrated the data using an empirical formula that was not uniquely mapped to relativity theory. There was no logical connection between relativity theory and the empirical expression.
Some engineers may have convinced themselves that they really used relativity. However, the empirical formula they used had too many adjustable parameters. So the is an infinite set of possible theories that could explain this empirical formula. 'Relativity' represents a subset of the many theories that could explain the empirical formula.
Some engineers were stupid in convincing themselves that they used relativity rather than an ad hoc expression. However, most engineers are bald faced liars.
The empirical formula used by the engineers is officially consistent with the experimental data. However, this official explanation is but a cover story. Relativity is internally inconsistent. So the engineers could not possibly have derived the empirical expression from relativity. Anyone can see that relativity is internally inconsistent, especially those with little education. So the engineers most probably lied when they said that they used relativity.
These liars either brainwashed or lobotomized all the other engineers and scientists. However, they probably lobotomized more scientists than they brainwashed. A brain washed person would still be smart enough to see all the 'obvious' contradictions in relativity theory.
Most engineers and physicists who insisted that there were contradictions in relativity were invited to several GPS workshops to help debug the software. Once in the room, they were strapped down. The prefrontal cortex of each scientist was cut out using dirty needles. Kaku did many of the lobotomy's with his own hand.
Some scientists were crippled. Stephen Hawking used to be one of the foremost critics of relativity before his lobotomy.
This drama of stupidity and corruption revolves the empirical formula used to calibrate the GPS formula. The empirical formula is the McGoffin and Bjarnes is the detective that no one believes.
The question you should ask yourself is whether the empirical formula can be uniquely mapped to relativity. We know relativity can be used to derive the calibration procedure. However, this doesn't mean that one can uniquely derive relativity from the calibration procedure. This sort of puzzle comes up regularly when one tries to 'invert' data. However, the engineers weren't trying to invert the data. Proving relativity was secondary. They just tried to make an accurate GPS system.
Many other conspiracy believers make the same assumption. They don't deny that the system works. They deny that the calibration technique has any connection with the general theory originally used to derive it.
Excuse me, I now have to adjust my aluminum foil hat!