Is it true that players might earn better ratings when playing the same course in a Tournament versus League play?

This is true in some cases. The roughly 2%-7% difference (1-3 throws) seems to be due to a little more pressure on players when playing tournaments versus leagues. Presuming the weather conditions are similar, it appears to be the most likely factor to account for the difference. The good news is that this effect doesn't help or hurt the ratings of players overall. No matter how difficult or easy a course plays, the average player rating of the propagators before the round is about equal to the average of the ratings they receive in each round. Check it out and see.