No they have not missed it - as
@danimal1211 shows in the post above. It is one of their premises for their argument.
All organisms that use NO3 as Nitrogen sources need to convert it to NH4/NH3 either just outside the organism or just at the inside before further transport and/or assimilation into amino acids. Its a energy demanding process that include different enzymatic processes. This is more or less an axiom.
Why using NO3 in this experiment instead of NH4/NH3 directly?
Its because NO3 is the predominant inorganic N species in oceanic water (and in water above reefs).
And this is my hobbyhorse when it comes to inorganic nitrogen sources in aquariums - this experiment not only proves zooxanthellae can take up inorganic N directly from the water column - it also shows they have the systems to convert NO3 into NH4/NH3 - IMO. Not all microalgae have this ability which will favour zooxanthellae (and the corals) if NO3 is the predominant inorganic N species in our reefs too. NH4/NH3 can be uptaken easily by most bacteria, micro and macroalgae and it is also true for organic amino acids that have the same or better permeation and transport capacity as NH4/NH3.
By using a fast nitrification and let the NO3 be the predominant N source - we will favour those organisms which have these enzymatic abilities to turn NO3 into NH4/NH3
Sincerely Lasse