I see.
That bit has not changed, but what follows should be a bit clearer...
This links back to the general Speaking Order rules. Basically instead of the Ref being the only one doing the Ref job... the Ref is the one with precedence, but then everyone else can have a chance to pitch in ideas and answers. The same happens in the Ref Phase, where the system basically asks questions to the players.
Thus, the Ref job is not a monolithic thing that needs to be passed around. Anyone can join in any time they feel like.
As mentioned somewhere else, having clearly defined roles is mostly for order and clarity. The group always knows WHO is supposed to say WHAT and WHEN. Once that is clear, they can easily behave in a more relaxed way, offering ideas at any time, if/when they feel like. Some groups benefit (or ever require) a more hierarchical order to feel at ease with the game. Some players have problems with (or categorically refuse to) engage with Ref-side activities while they are still also playing as Delvers. For them this structure is beneficial.
For others (maybe your group?) it's more like a vague guideline to follow by feeling ;-)
In the case of this specific game element, as long as your group feels good with it, it's all good. The important bit is avoiding that same person asking a question and offering the answer too. That is usually quite boring and shifts the experience too much towards "shared storytelling" rather than an actual game where you get challenged and surprised.