I am afraid there are 2 things you are confusing here:
1. The "actual spacing" of a rebar layout rule is different from the "user input spacing" or the Rebar.MaxSpacing you can find in Revit Lookup tool or through API (yes, I see you did work with Revit API). The "actual spacing" is the actual distance between 2 continuous bar in a rebar set, that is calculated from rebar set Array Length and number of rebar (quantity). Depend on the rebar layout rule, the "actual spacing" may varies from the "user input spacing":
- Maximum Spacing: the "actual spacing" is less than or equal to "user input spacing".
- Number with spacing: the "actual spacing" is exactly the same as "user input spacing".
- Minimum Clear Spacing: the "actual spacing" is greater than the "user input spacing"
You can look up the RebarLayoutRule enumeration in API docs for explanation. Further more, the "actual spacing" is the distance from the same point of the current rebar to the same point of the next rebar in rebar set (as you have rephrased "center to center", depend on how you define "center"). This "actual spacing" does not minus the diameter of the bar.
Reproducable case: create a rebar set and change layout rule to "Number with spacing", then chcange the spacing to less than rebar diameter, put a linear dim between centers of 2 continuous rebar of that set, you 'll see.
2. The thing I was struggling with is not "why the user input and the actual spacing are different", but it is "I know it must be diffferent, but why choose this arbitrary value for actual spacing when there are other values that makes sense and more predictable?". I just want to find out how to calculate the actual spacing / rebar quantity for MinimumClearSpacing layout rule. I did believe you have some hints or suggestions about this, but it turned out we are both quite far from it.
Regards.