In the first part of this episode, it is announced that the $1000 offer to ride the bull is good for Diablo's entire stay at the Bar A ranch. However, Buchanan reminded the Cunninghams in this part that the offer is only good during the rodeo. He does decide to "bend" the rules, rules that were not being broken.
When Fonzie was supposed to be in the barrel, the bull knocked it over and you could clearly see that he wasn't in it. There was something grey - possibly a sack. Also, when the bull was knocking the barrel around, you could see it was empty.