Ven Analayo is correct in saying that Jhana is too refined a state to investigate anything.
The common ground that the two venerables have missed is that some references to Jhana in the suttas make more sense from a practitioner’s perspective when read as a process rather than a particular attainment or state of mind. In other words, the word Jhana can incorporate the process by which it was attained. The commentators, such as Buddhaghosa, recognised that understanding this point was not always clear and so defined Samadhi as three steps, Khanika, Upacara and Appana, where Upacara is a preliminary or conduit to Appana. So when the word Jhana is used it can include Upacara as Upacara may be a pre-requisite.
In the reference
samma samadhi does not refer to the state of Jhana. It refers to Upacara Samadhi. In Upacara Samadhi, the mind is focused on a single object (immersed?). This state, like the conventional world, is a duality - the observed object and the observer. When Appana is achieved, the object disappears and there is a singularity. The observer observes itself. This state is tranquil and still, too still to be involved in investigation.
The translation of Samma Samadhi as “immersion” when referring to Appana is, I think, misleading. “Immersion” implies duality - that which is immersed and the medium in which it is immersed. As Appana is a singularity, the definition “immersion” seems out of place.
I hope this helps.