One does have to regulate the intensity of training a bit ie. some days you really go for it and other days you may be phoning it in a bit...but in training circles that is considered active rest.
If you read the coaches corner part on MMA, the foundations and the linked articles on the time scale of training adaptations you will see that the metabolic pathways which are utilized during BJJ are what is primarily trained in crossfit. It does break with tradition a bit... but the science makes sense and more importantly... it works. If you have ever watched the documentary "Choke" you see Rickson doing sprints up stairs and gymnastics. Chack out some of the training advocated by matt furey, steve maxwell and others...most of the good fighters do intense interval training and rely on slower technique based mat work to in place of long distance running.
Hope this helps.