There's a hypothesis that this is why we (normally) forget our dreams; it prevents us from getting confused about what's real.
Analogy: a magical secretary is tidying your desk and files. They pull out some files to re-order, put some files you were working on away, lift it pages/images to see where those files should go, etc.. You interrupt them and they scuttle away. You don't believe in magical secretaries so you quickly (and inconsistently) imagine that you were working on the files that were out making a story that explains how those files came to be there, in that arrangement.
Presumably if scanning techniques can show images of what we see in dreams that provides some evidence against this hypothesis, however it doesn't defeat it unless it shows we _experience_ those images through the period when we suppose we're dreaming.
Evidence that refutes this idea gladly considered.
Another possible argument against is if a partner next to you observes you tossing and turning and possibly speaking in your sleep over time, and then you wake up and describe a dream you were experiencing consistent with what they saw. How would you explain the tossing and turning and talking in one's sleep in your hypothesis?
So at the very least lucid dreams happen in 'real time'.
People saying things could be like the images appearing in the visual cortex that I tried to address in brief. They can appear, be processed, provide external output and such without necessarily being part of a dream experience happening at that time.
Back to my analogy, the magic secretary plays back some sound files, which maybe someone in a different office hears and attributes to you being present, but which you aren't "there" to experience. When you start to wake to consciousness you see the files and infer you were working on them, your partner mentions utterances consistent with one file and your brain meshes that in to part of the "story" it is writing of the dream experience (a la deja-vu).
See however the sibling comment.