AT THE GENEVA arms talks, the Soviet government is demanding more in the way of on-site inspection and the American government is demanding less. This marvelously ironic reversal of traditional positions on verification is taking place in the negotiations on a treaty to ban medium- and short-range nuclear missiles -- the treaty that is the likeliest candidate to become the Reagan administration's first and perhaps only arms control accord.

On-site verification, as distinguished from verification by ''national technical means,'' has been an American aspiration for even longer than it has been a formal American negotiating demand. It has been seen as a safeguard against Soviet perfidy, and it has become central to the politics of arms control. That the Soviets long resisted on-site inspection, denouncing it as a mask for espionage and as a practice made unnecessary by satellite intelligence, tended to confirm its value in many American eyes.

But it is not simply that Mikhail Gorbachev, with his sudden strong favor for on-site inspection, has now called an American bluff. Officials explain, plausibly, that once the Kremlin agreed to elimination of intermediate-range missiles worldwide, and not just in Europe, the problems of verifying an agreement became simpler. Further, they found that the Kremlin might reap unacceptable intelligence advantage from ''challenge inspections,'' the particular form of anywhere, anytime verification that the administration has most emphasized.

In fact, paralysis is a predictable result of applying high monitoring standards to reductions of the kinds of arms -- small missiles or warheads, for instance, and chemical weapons -- that defy such standards. Moreover, inspections of any sort cannot resolve the most common breed of Soviet-American arms control tensions; these flow not from limits on verification but from inadequate treaty texts or from open political defiance -- for example, the Soviet radar at Krasnoyarsk.

The reversal in Geneva puts pressure on Mr. Reagan to reassure Americans stirred to wonder whether he is taking unnecessary risks. It will probably be a source of some political embarrassment to a president who had sworn he would write a treaty inscribing comprehensive rights to search for hidden weapons. Still, the embarrassment is evidence of a realistic trend in official thinking. It would be much more than an embarrassment -- it would be a scandal -- if an American president allowed a particular notion of verification to get in the way of a useful treaty