I think the basic confusion is a contradiction between two uses of the word "choose", and hence of "swap".
I can dither in winter between Ibiza and Majorca for my summer holidays, choosing Ibiza one day, swapping it for Majorca the next, and swapping back again to Ibiza the day after, and so on endlessly, or at least for a week or two. But although I've used the word "choose" here, it's equally true to say the opposite, namely that I've actually failed to choose as long as I fail to take any action that changes things irreversibly, such as make a booking. And if I haven't made a choice, how can I swap it?
Similarly if my choice of envelope doesn't result in any irreversible change, for example going on to be offered a further choice between a further pair of envelopes, one which is half and the other double that original choice, then to say that I've chosen and swapped anything at all is to say no more than I've dithered, just as in my holiday resort example.