The reaction of hypochlorous acid (HOCl) solutions with silver oxide only liberates oxygen and produces AgCl.
When chlorine reacts with silver oxide diffused in water, a mixture of silver chloride and silver chlorate is formed.
Silver nitrate can react with sodium hypochlorite to form silver chloride and silver I,III oxide, Ag2O2, is formed, both of which are precipitated. An unknown substance, with bleaching properties, is left behind in the solution. This substance is unstable, and quickly decomposes after several minutes, leaving behind silver chlorate in the solution, which does not bleach. If sodium hydroxide is added to the bleaching substance, oxygen gas is evolved.
However, silver hypochlorite may also be formed from the reaction between silver nitrate and sodium hypochlorite, according to the same book.
If a solution of chlorine is added to excess Ag2O, silver hypochlorite can be formed in solution. AgOCl partially decomposes in darkness, or rapidly if heated above 60degC, into AgCl and AgClO3.
A comprehensive treatise on inorganic and theoretical chemistry, Volume 2 By Joseph William Mellor. p271
The bleaching substance is probably a mix of ClO2 and HOCl. Although it is really rather speculative on my part, I think the reaction might look something like:
(6)AgNO3 + (6)NaOCl --> (6)NaNO3 + (4)AgCl + Ag2O2 + (2)ClO2
The formation of oxygen from the addition of NaOH to the bleaching substance probably only occurs in the presence of excess AgNO3 still disolved in solution. If this is not the case, I cannot see any plausible way that any bleaching compound could be produced in the reaction which would react with NaOH to produce oxygen. One would expect that an excess ratio of AgNO3 had been used, since if there was any excess NaOCl not reacted, then the investigators would not have been able to determine that there was a new bleaching substance that had been formed (since NaOCl acts as a bleaching agent itself). It is, for example, known that Ag2O reacts with HOCl to form AgCl and oxygen gas.