But why would he say that it is easier during your boost week?
I'd say 3 reasons:
1. During your boost tourneys, you typically put in more resources to get further in the tournament. Therefore, in the back of your mind, you're always "winning more" during your boost tournament. But few people are keeping meticulous track of catering costs, or troop losses, so they don't know whether winning more actually cost them as much.
2. Depending on your progress through the game, you may only have 1 tourney at a particular squad size tech. Meaning you research Squad Size Upgrade 7 during a marble tourney, and by the next time marble comes around, you may have researched Squad Size Upgrade 9. And so you did Marble, Steel, Planks, and Crystal at 7, Scrolls, Silk, and Elixir at Squad Size 8, and Dust, Gems and Marble at Squad Size 9. During all of these tourneys, you're remembering how you did, but you're not considering how much harder each tourney got from each Squad Size upgrade. So you "remember" how well you did during some of those boost weeks, but you don't properly put it into perspective.
3. Its something he heard, and it just gets repeated over and over. No one tests it and the math of catering costs (and the realities of certain enemy compositions) make it hard to definitively test. So a rumor becomes a fact.