As a Platinum player, I destroy players in silver/bronze on smurf.
The problem with the diamond player who posted he was having a hard time in lower elo smurf is that he approach lower elo games with the same mindset as higher elo games.
For example, in plat/diamond, you play very safely, with big vision coverage and not too many engages, more often than not, you'll see the mid or top laner drop their opponent to 1/4 health and disengage because they see or expect the enemy jungler to be around.
In bronze/silver games, as a higher elo player, you need to go balls deep, pushing EVERY advantage you got and being overly aggressive ( similar to how, let's say, fabbyyyy plays in high elo, which surprise some players and allows him to get ahead more often than not. You have better mechanics, game understanding etc than lower elos player as a diamond/platinum or even gold, you're supposed to more or less be able to predict jungle pathing, as they usually take the bad ones, thus, you can push your advantage, get fed and profit from other lanes not being as good as you to get fed on them as well.
I expect this post to get a lots of downvotes, but I hope you can be impartial and understand that Im not trying to be arrogant, but just to show that, if this "diamond" player has problems beating lesser skilled players, he's either not good enough for his rank or has serious problem adapting his play style to the situation.
Kindly.