They found (weak) evidence of change. In order to confirm constancy, they would have to find significant evidence of no change.
This is not accurate. In the paper, the authors state that they are not able to conclude, so they suggest that more precise measurements are needed. Moreover, it is not possible to prove that there is no change by experiment. One can only demonstrate the effect, or determine an upper limit for it.
Are we running light with overbyte?