I find that the problem does not occur when I switch to MME drivers instead of ASIO in RealBand audio preferences.
But I want to emphasize that Band In A Box does not have this problem. MME is a cumbersome workaround but I suppose I can live with it until the problem is fixed. I cannot monitor input with MME drivers.
So if someone at PGMUSIC can figure out why Band In A Box can use ASIO just fine, but RealBand generates distortion I would appreciate it. Even playing a VSTi instrument generates the distortion in RealBand, not just recorded material.
Bottom line is that RealBand has a problem with ASIO where the sound has lots of distortion. Band In A Box does not have this issue.