It’s also odd that the nurses and others at the hospital didn’t see Daniel leave with Howard - they only saw Howard.
I think, for whatever reason, it was Howard who told Anna that Daniel had gone with him, when she didn’t remember “details” of that night, post-trauma.
That way, whatever happened to Daniel “could’ve” happened when Daniel “left the room/hospital” and the cause of death wouldn’t be confined to just the contents of the room, if you see what I mean.
I think either the nannies are fibbing about that particular detail, or Anna thought she remembered that and thought wrongly. I don’t think Daniel ever left the hospital.