If I publish a level with a memoriser or object saver in it, and a person plays it, it will load that data again next time they play, of course.  What happens if 2 players, who have both already played it and have data saved, play together in the level?  Which one will it load?  And then will it save the same thing onto both systems?
(I'm building a survival level that would save the player's best time and compare it next time they play.  It will be a Versus level up to 4 players, so this is kind of important.)

I think it will only load the host's save data, and I think it will only save onto the host's system. I'm not too sure tho.

Good luck in the building of it!

Nope, memoriser and object saver DOESN'T save progress for every player. Progress is being saved for host only. That means player cannot transfer their data so it can be used by that player as a host or as a member of any other host's sessions later on. Which is such a huge disadvantage of saving tools, because there would be lots of possibilities with this option (especially for multiplayer type levels).

That's a shame. I understand that it would create big complications for the developers to include something like that, but it would be nice to be able to save data for each player. I guess I'll just add that to my already huge wishlist for LBP4, lol.
For this level, I think I might let it save their best time if they play solo, otherwise just show everybody's time and not save anything.