Based on the information shared and available there mostly three more possibilities.
- There is a make break switch that is triggered based on the battery packaging. Review the original battery package as well as the housing compartment for specific mechanical features associated with a trigger. Below are some battery packs that are similar to original.
The battery system might have something similar to a Reed Switch. In such situations the mechanical package would have a small magnet embedded, that is been read by a proximity sensor which triggers the charging system.
As complicated it is there is a real possibility that battery charger has intelligence to detect between a non-rechargeable primary cell battery and a rechargeable battery prior to enabling battery charging. In the Sony MRD-IF240RK has following statement provides some evidence. Check the Sony MDR-RF4000K manual for similar statements. If so the eneloop battery might not be satisfying the electrical specifications.
Technically there are designs similar to the one below that can detect a rechargeable vs non-rechargeable batteries.
How this done is based on the internal resistance of the battery? Below except should provide some insight the methodology.
The typical internal resistance for new high-capacity NiMH rechargeable AA batteries is between 30mΩ and 100mΩ, and for an alkaline battery it is usually between 200mΩ and 300mΩ (but as high as 700mΩ, depending on its charge status). Faulty rechargeable batteries have a much higher internal resistance. The DS2711/DS2712 chargers therefore calculate the internal resistance of batteries to be charged, using the measured battery voltages (VP1 and VP2) and the charging current that has been set.
Therefore there is high possibility that the Internal Resistance Eneloop NiMH battery is outside of the chargers technical specifications.
Additionally Stefanv.com in article Electronics Reviews has some interesting observations including the follow for Eneloop NiMH batteries
Lower internal resistance, meaning higher voltage reaching equipment that uses high currents
A final point to note. The combination of internal resistance and charge current causes change in temperature inside the battery. As you would imagine high temperature affects the battery adversely. Most modern charging IC have a temperature monitoring system as part of system safety.
Full and other related articles can found in the reference sections.