Yes, but it's not exactly the same situation. "The EPA’s equipment isn’t able to detect lower levels of Butyl Acrylate that can still pose a threat to human health." In Chernobyl, the Soviets had the opposite problem: the maximum concentration their standard equipment could read was far below the real level.
Unfortunately this is not the case with many Geiger counters, especially older ones. Geiger-Muller (GM) tubes detect radiation by measuring ionization events. When a high energy particle passes through the tube, it leaves a little trail through which electricity can flow, but only for a moment — this temporary flow of electricity is amplified and fed into the detection circuit, and it also what is used to generate the typical clicking noise. The Geiger counter is basically an edge detector + summing circuit with decay.
When a GM tube is overloaded, the particles create too many overlapping trails, and the tube cannot stop conducting electricity. This continuous flow of electricity does not trigger the edge detector, so it thinks the level of radiation is zero. Some modern equipment has an alarm for this condition.