ediblelandscapingsc,
I agree with you and Mike that a fan cannot rebloom unless it has bloomed a first time, I am just not sure that the AHS rebloom definition is limited to a single fan! I agree with Donald and Maurice also, in my garden any bloom that shows up after the initial first flush of blooms is adding to the length of bloom display and I considered that to be rebloom. I would even consider a proliferation that created a new scape and bloomed to be rebloom,... (proliferation rebloom)?
Now taking my last view to the extreme, if I purchased a plant from a nursery and that plant was a new fan or fans produced by the mother plant, later in the year I went back and bought more fans from the same mother plant and planted those in my garden, they later bloomed? Now would that be rebloom?
One of the main reasons I look for daylilies that are described as by terms like "fast multiplier" is not because I want two dozen new fans to sell (I don't sell plants) I am looking for all those scapes to come shooting up and displaying new "rebloom". The drawback certainly is that you do have to keep thinning out those plants regularly or the clump will become too large. I have seen people specifically avoid plants that multiply rapidly, so how a plant "reblooms" would indeed be very important to them and I think maybe the method of "rebloom" should draw more attention. Single fans reblooming would be a much better type of rebloom for people with limited space.
