Absolutely, the viscosity results can be different between two different models of viscometer/rheometer using the same spindle, same rpm, same material/concentration, measured at same temperature, and same exact sample preparation procedure used for each product being measured.
One reason is that the springs inside are not rated the same. For example, the Brookfield DVII+ viscometer/rheometer comes in LV (Low Viscosity) and RV models (Regular Viscosity) with the torque constant for the LV at 0.09373 and torque constant for RV being 1.0 so in effect the LV model is over 10 times more sensitive (1.0/0.09373) for use with lower viscosity samples. Even with same model, two viscometers could give slightly different results if one or both are out of calibration (but likely not 3000 vs 4500 cP unless one spring has been irreversibly strained and needs replacing).
Our QC department had similar issues between our viscosity results and an ingredient supplier and the investigation turned up that the instruments used to measure (both Brookfield LV models) were calibrated well, but temprature was a factor (one country cold and other tropical) but most significant factor affecting variability was the different sample preparation SOPs. So I would say try to find out your model's torque constant, run some silicone oil viscosity standards within (3000-4500 cP range) to test your instrument in conjunction with the other company's instrument. Then if instrument spring's are comparable, start comparing step-by-step the sample preparation procedures.