We had a DRII in a couple of weeks ago which the owner wanted revalving and servicing. I assume this wasn't yours as this one sounded fine.
If the problem is only on the distortion channel it is very unlikely to a problem with the output stage.
Without looking at the amp my guess would be that there is either a problem with a component in the preamp (unlikely but should be easy for a competent tech to find) or a problem with the channel switching. The switching on the DRII uses optocouplers which are not the most reliable devices. Also the way the switching is implemented means that the switching elements have a filtering effect on the guitar sound. Interestingly using the footswitch changes the distortion channel sound when compared with using the switches on the front of the amp. Unfortunately many "techs" don't really understand how the switching works on a DRII.
I am amazed that amp techs can get away with not telling customers what they have done to an amp (although I often think that this is due to the fact many of them don't know what they are really doing), and can charge for not fixing something. If we can't fix it at an economic cost we don't charge. We also always return any parts we have removed from an amp.
Anyhow if you don't want to throw more money at a repair shop you could try changing the optocouplers in the amp (use two Vactrol VTL5C1s), although without looking at the amp I can't be 100% sure that this will work. Also you must ensure the polarity is correct.
If the optcouplers are not the problem changing them won't cure the problem but won't do any harm, however if you botch it and make the situation worse you will have to take it to an amp repairer who may take a dim view of your attempts to repair it........
Anyhow there is some useful info on Rivera era amps on this site:
http://www.geocities.com/twoseriesfenders/index.htmlGood luck and let us know how you get on.