That is indeed complicated, but that hypothesis isn't what Yvain was suggesting. The proposed adaptation is just that memories don't get stored as usual during REM sleep, which is a relatively simple thing for the brain to do. (Also, it's pretty clear that this actually happens.) It's then argued that this is a good adaptation for evolutionary reasons, because if we lacked it (and kept the rest of our tendencies of believing every conclusion we remember, context notwithstanding) we'd have some problems.

(E.g. an ex-girlfriend of mine who would stay angry at people who had been mean to her in her dreams, despite knowing that it had just been a dream.)