There is no proof of this.
The fact is there are thousands of people doing fates and leves which generate gil into the economy. This is happening every minute of every day.
The small percentage of people who have a high repair cost have blinders on and think they should be able to do fates and leves to cover their repair costs (or worse, have dungeon runs give them gil for doing them). They don't realize that its the economy as a WHOLE which determines how much gil is being created. The gil sink from their repairs is actually very small compared to the gil created by those thousands doing fates/leves all day long.