@evanEvan Prodromou To be more explicit, I think I understood your explanatory reply to your original survey but wanted clarification that the repeated word "it" was referring to the user's browser, or perhaps "the user's browser running javascript loaded in the page fromm a.example".
Your first sentence response to my question seemed to confirm this. But then your followup about server-side or client-side made me wonder if my contra-example of a.example proxying interaction with b.example was correct.