I have found the opposite, I think it really boils down to what kind of dirt pedals you're using. I've had no luck with a Tri-AC playing well with an Ibanez PD-7 with anything but Clean, and even then it's super noisy, but I've had great luck with the Bass Driver playing with it. Likewise, I've had great luck with the Tri-AC playing well with a Guv'nor overdrive clone, but no luck with the Bass Driver playing well with it. I've had great luck with both and a modified Boss DS-1.
The Drive knob is your best friend. On the Bass Driver, I usually left it at about half or lower when using overdrive with it. However, if you're using the SansAmp without cabinet emulation, I could see how it wouldn't work well at all.
Edit: I think it depends a lot on the bass/cables/pots you use as well. Not all cables are made equal--some are much noisier than others.