what exactly are you measuring? A sine wave, or some broadband modulation or digital signal? You would want to measure a stepped sine wave...i.e. CW tone, make the measurement at 60 MHz, step freq to 61 MHz, remeasure, and so on.
Also, is there some isolation between the splitter and the DUT? like an amplifier with low S12? The reflected group delay of the DUT might be pulling the apparent time of the C1 reference, causing erroneous group delay measurement.
I know that modern Tektronix scopes display the true time relationship of all channels, I have carefully confirmed that. What scope type are you using?