Excellent question. It's not the higher rated player, it's the player who is playing at a higher level of skill during the simulated tournament.
There's a subtly in the model that eliminates the day to day variation in skill level that players experience. In real life, a player might play above or below their rating on any given round for two reasons: One, they are actually playing better (or worse) because the course suits their style (or not) or they are hungover, or any number of factors that affect their play. The second reason is that for a given level of play, there are random results. Sometimes the disc that hits only nubs goes in and sometimes it rolls away. Sometimes the disc barely misses a tree, and sometimes a puff of breeze will knock it into the hanging dead branch.
I eliminated the first variation. In the model, when a 1005 "rated" player is pitted against a 995 "rated" player, each player's expected score on every hole is based on their skill level that day. For example, the 1005 rated player will have a better chance of getting a two on every hole.
The actual score is randomly selected from each player's expected distribution of scores for that hole. As a result, the player who is playing higher rated golf that day doesn't always get assigned a better or equal score on each hole.
In other words, before the simulated players get started, I know exactly at what skill level they are going to play, so I know who should win. A tournament (with tiebreaker) has failed to do its job if it didn't identify the player who I know was playing better that day. That's why I use the correct/incorrect terminology.
Thanks for the clarification.