Regarding the discussion of gradual accumulation of residual nitrogen over multiple days of multiple dives, which has a direct bearing on general recommendations to take some kind of break every 3 or 4 days:
I think this statement (bolded, to preserve context) is the fundamental issue:
The point in discussion, is the long held belief that we divers accumulate some excessive tissue saturation over several days, and that directly causes injury. But that acumulation is not the case. If the basic on / off gassing formula are to be trusted, then they show the build up does not exist.
The fact is, those formula are NOT to be trusted. They are to be accepted with high confidence, but not complete 100% confidence.
The formulas are a mathematical model intended to predict inert gas buildup in a diver's body. But, every person's body is different. Some people's bodies exactly match the model's predictions. Others' bodies don't match very well at all. Some people will match the formula well on one day, but not match well at all on another day. As one example, they may match well when they are well hydrated and not match well at all when under-hydrated.
If a particular individual varies from the model by retaining 10% extra nitrogen (I'm speaking in very simplistic terms here - this is Basic), then, at the end of 1 day, they aren't that far off from the model's predictions and are probably not going to experience symptoms of DCS. But, when you compound that personal variation over multiple dives per day for multiple days, then the difference between what the model PREDICTS and the actual state of the person's residual nitrogen load is going to become larger and larger. To the point that they could become very susceptible to DCS.
It's like being off in aim by 1 degree. If you're shooting at a target that is 10' away, you will still hit the bullseye. But, if you're shooting at a target that is 100 yards away, you're going to miss. The end of your first dive is the target that is 10' away. The end of your 20th dive in 5 days is a target that is 100 yards away.
I think recognition that the "formula" are just estimates - educated guesses, if you will - is key to understanding why it is important for divers - and especially divers on the less experienced end of the spectrum - to give themselves a break every few days. Even though the "formula" may predict that it is not necessary.
There is only one time when a dive computer OR TABLE has it's maximum accuracy and that time is when you have not been diving for a while - i.e. greater than 24 hours, AT LEAST. Taking a break every few days lets your body and dive computer both reset back to a known "good" state - to the state where body and computer match most closely. Your body gets back to (more or less) "zero" and the computer does the same. In other words, the break is when your body "walks forward" and gets up to 10' away from that target that was 100 yards away.