We re-analyse earlier measurements of resistance R and piezoresistance K in RuO2-based thick-film resistors (TFRs). The percolating nature of transport in these systems is well accounted by values of the transport exponent t larger than its universal value t ≈ 2.0. Furthermore, we show that the RuO2 volume fraction dependence of the piezoresistance data fit well with a logarithmically divergence at the percolation threshold. We argue that the universality breakdown and diverging piezoresistive response could be understood in the framework of a tunnelling–percolating model proposed a few years ago to apply in carbon-black–polymer composites. We propose a new tunnelling–percolating theory based on the segregated microstructure common to many TFRs, and show that this model can in principle describe the observed universality breakdown and the diverging piezoresistance.