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It istrue that the current (Block II) satellites carry clocks which are occasionally adjusted from the master ground control station.

It is completely false that the GPS somehow defies the predictions of relativity theory. Indeed, when the first atomic clock was sent into orbit in June 1977 (aboard a satellite which was a testbed for the Block I GPS), and I quote from Ashby's paper:
there were some who doubted that relativistic effects were real. A frequency synthesizer was built into the satellite clock system so that after launch, if in fact the rate of the clock in its final orbit was that predicted by GR, then the synthesizer could be turned on bringing the clock to the coordinate rate necessary for operation. The atomic clock was first operated for about 20 days to measure its clock rate before turning on the synthesizer. The frequency measured during that interval was +442.5 parts in 10^12 faster than clocks on the ground; if left uncorrected this would have resulted in timing errors of about 38,000 nanoseconds per day. The difference between predicted and measured values of the frequency shift was only 3.97 parts in 10^12, well within the accuracy capabilities of the orbiting clock. This then gave about a 1% validation of the combined motional and gravitational shifts for a clock at 4.2 earth radii [the radius of the satellite's orbit].
It is true that GPS is not used as a test of gtr, because it is simply not designed for that purpose. In particular, the orbiting clocks are occasionally reset from the ground to maintain the best possible synchrony of the orbiting clocks with one another and with UTC time.
It is completely false that the design of the GPS system ignores relativity theory. Relativistic effects in the GPS system are vitally important. The total difference in the rate of atomic clocks on board a GPS satellite and the reference clock at the USNO amounts to some 38,600 nanoseconds per day. (This is mostly due to a combination of the Sagnac effect for a clock which is moving wrt the GPS receiver, and the relative gravitational time dilation between a stationary clock on the Earth's surface and a stationary clock 20,200 km above the surface, as mentioned in the above quoted paragraph from Ashby's paper; frequency shifts in clocks on the ground wrt UTC due to inhomogeneties in the shape of the Earth also play a role.) In contrast, in order to maintain the accuracies listed above, the GPS system must maintain a timekeeping synchrony within 10 nanoseconds variation per day, indefinitely! The major way in which the 38,600 nanosecond per day discrepancy due to relativistic effects is accounted for is by building into the GPS software used to keep the satellite clocks in synch with each other and to synchronize GPS time with UTC an effective downward frequency shift of 446.47 parts per trillion in the orbiting atomic clocks. In addition to this basic conversion factor, GPS receivers are programmed to take account for the fact that slight eccentricities in the satellite orbits result in tiny periodic changes in the frequency of the orbiting clocks.