You're right, it does seem counter-intuitive.
It's late so this is just off the top of my head. Perhaps the Quickie volume control has a poor contact, and maxing it out takes it out of the signal path? Some contact cleaner might answer that question.
Normally I would expect Quickie to get distorted only when over-driven. Its internal noise however will be independent of its level control, which just attenuates the input. So your new arrangement would increase the distortion and reduce the noise of the Quickie - again, going by usual practice and assuming there is nothing strange going on.
There is some chance if the Quickie is driven to its maximum but not much beyond, that it can act as a limiter by soft clipping - which allows the power amp to produce greater sound level without going into hard clipping as solid state amps do. If the t-amp is not especially powerful, or you speakers are not very efficient, this is a possibility.
Well, just some thoughts.