Hey, @drbenvincent!
Thanks a lot for your response, appreciate it!
This sheds much light to how the approach works, but I would follow-up with one question, if you do not mind.
Regarding the cumulative intervals growing with time:
Would it be correct to say that, if posterior predictive distributions (would theoretically) have absolutely the same distribution, cumulative interval would not widen with time, right?
PS. Just after reading your answer I came across this article of yours.
I would recommend it to anyone coming to this thread.