Interesting question! One example of "scientific meddling" might be the precogs themselves, whose natural talents have been honed in a government training facility; with the technology Precrime possesses, the precogs are harnessed, mutated, and put to use—not healed. Does anyone pay for their treatment of the precogs? One could argue that in the end it's Anderton's own system that punishes him; foreknowledge of his own crime is to some extent what actually leads him to commit the crime.
Anderton's flawed system also introduces another aspect of scientific meddling, I think, with the computer system that seeks commonalities between the three precogs' predictions. Occasionally, as we are brought to realize, there is no majority report; all three reports may differ so significantly as to be three minority reports (three alternate futures?). But the computer, programed to seek commonalities, pieces together a majority report of its own accord that doesn't always take into account the possibility of deviation suggested by the minority reports (and which the authorities then act on). Does that mean people are punished for crimes they might never have committed? That would indeed be paying for scientific meddling.