I also agree with your conclusion, from the information at hand that seems to be the most likely event.
If I may present a counterargument to your counterargument: *Crazy theory rambling starts*
It's likely that the individual spren bonded to the Radiants knew (because of the bond they shared) and were in agreement about what had to be done, i.e. the Recreance, but isn't it possible that the spren that reside in the cognitive realm didn't know and were therefore pretty upset what with all the mass betrayal and such? While I can't really present any concrete facts to support this, from what we've seen so far neither Wyndle nor Syl seems to have any contact with the Cognitive realm.
Edit: But why wouldn't the Radiants check with the Cognitive realm first, surely they must've been able to, or maybe they didn't think to check it first because they weren't aware of the repercussions for the spren.