I just read something that seems salient here. The Spanish book I'm reading explains that dejar + inf. is used to express "to allow to, to let".
One example (which led me to revisit your post) was "Dejé caer mi libro." ("I dropped my book.")
This would seem to be an analogous situation to your post where you could say "Dejé caer mi libro." or "Se cayó mi libro."
From my very non-expert point of view, it seems to be an active vs. passive pattern.
"Dejé caer mi libro" = "I dropped my book"
"Se cayó mi libro" = "My book fell"
Therefore, this seems to validate what you said:
"Se dejó caer de rodillas" = "He dropped to his knees" (active - he intentionally allowed himself to drop)
"Se cayó de rodillas" = "He fell to his knees" (passive - he involuntarily fell)
Maybe I haven't added anything substantive to what's already been explained by native speakers, but I thought it was interesting and wanted to share :)