And to back my previous post up more, this episode really didn't even need to do the pity badge. Looking at past episodes:
1. Brock: Ash didn't have any Pokemon that could gain him the upper hand. The more experienced Ash could have had Pikachu using Iron Tail (which didn't exist at the time) and take advantage of Butterfree being able to learn Confusion.
2. Misty: Pikachu wouldn't fight, nor did he have a really strong Pokemon, so okay.
3. Sabrina: Psychic Types were quite the power house back then, so it would take a lot for Ash to credibly win.
But with Erika, her Pokemon while decent weren't overly strong, nor was Ash lacking adequate Pokemon. Heck, he had two which had the type advantage and would gladly fight for him. So there was really no reason that they couldn't have him make a legitamite win.