Labyrinth chest
I personally doubt it and believe that the reason people think it does is because to get to tier 3 requires a lot of people and with the more people there’s an increase of chance of encountering someone on that map of getting good loot. It’s more of an illusion.
Unfortunately we really can’t prove or disprove whether the tier actually affects the drops. There really hasn’t been any tests comparing a tier 1 to a tier 3 that have a large enough sample size to be reliable.